M.C.Q. [1 Marks Each]

MCQ 1511 Mark

Mark the correct alternative in the following question:
The perimeter of a square whose area is $225m^2$ is:

A
$15m$
✓
$60m$
C
$225m$
D
$30m$

Answer

Correct option: B.

$60m$

We have,

Area of the square $= 225m^2$
As, the side of the square $=\sqrt{\text{Area}}$
$=\sqrt{225}$
$=15\text{m}$
So, the perimeter of the square $= 4 \times side$
$=4 \times 15$
$=60m$

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MCQ 1521 Mark

Length of a rectangle is $8cm$ longer than its width. A square of side $x$ centimeters is cut out of it. If $x$ centimeters is half the width of the rectangle, then the remaining area in square centimeters is:

✓
$3x^2$ $+ 16x$
B
$2x^2$ $+ 8x$
C
$3x^2$ $+ 8x$
D
$2x^2$ $+ 16x$

Answer

Correct option: A.

$3x^2$ $+ 16x$

If width = W, length $= 8 + W$
$\text{w}=\frac{x}{2}......\text{given}$
Total area of rectangle = $W (8 + W)$
$= 2(8 + 2x)$
$= 16x + 4x^2 - x^2$
$= 3x^2$
$+ 16x$

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MCQ 1531 Mark

Mark $(\checkmark)$ against the correct answer in the following:
The cost of putting a fence around a square field at $Rs. 25$ per metre is $Rs. 2000$. The length of each side of the field is:

A
$80m$
B
$40m$
✓
$20m$
D
None of these.

Answer

Correct option: C.

$20m$

Total cost of fencing around a square field $= Rs. 2000$
and rate $= Rs. 25$ per metre
$\therefore$ Circumference $=\frac{2000}{25}=80\text{m}$
$\therefore$ Length of each side $=\frac{80}{4}=20\text{m}$

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MCQ 1541 Mark

A pentagon has three sides with length x, and two sides with the length $3x$. If $x$ is $\frac{2}{3}$of an inch, what is the perimeter of the pentagon?

✓
$6$ inches
B
$7$ inches
C
$9$ inches
D
$12$ inches

Answer

Correct option: A.

$6$ inches

$6$ inches : The perimeter of a pentagon is the sum of its five sides :$ x + x + x + 3x + 3x = 9x$ If $x$ is $\frac{2}{3}$ of an inch, the perimeter is $9\big(\frac{2}{3}\big)$

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MCQ 1551 Mark

The perimeter and area of square is same. find its side:

✓
$4$
B
$8$
C
$16$
D
$64$

Answer

Correct option: A.

$4$

Let the side of square be a
Perimeter is $4a$
Area of square is $a^2$
According to question $4a = a^2$
$\Rightarrow a^2$
$− 4a = 0$
$\Rightarrow a(a - 4) = 0$
either $a = 0 or a =4$
$\therefore 0$ cant be taken as a measure length

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MCQ 1561 Mark

The perimeter of a rectangle is twice the ........ of length and breadth of the rectangle:

A
difference
✓
sum
C
product
D
None

Answer

Correct option: B.

sum

The perimeter of the rectangle is the sum of all sides that is $2 \times $ length $+ 2 \times $ breadth So, we can say that the perimeter of a rectangle is twice
the sum of length and breadth.

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MCQ 1571 Mark

Perimeter of a rectangle is measured in .........

A
Sq units
B
Cm units
C
Cm
✓
Given units

Answer

Correct option: D.

Given units

Perimeter is measured in the given units of the length and breadth of the rectangle.

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MCQ 1581 Mark

Perimeter of a square whose side measures 4m is:

✓
$16m$
B
$16cm$
C
$4m$
D
$12m$

Answer

Correct option: A.

$16m$

We know, Perimter of a square
$= 4 \times $ Side $= 4 \times 4 = 16m$

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MCQ 1591 Mark

If the sides of a square are halved, then its area.

A
Remains same.
B
Becomes half.
✓
Becomes one fourth.
D
Becomes double.

Answer

Correct option: C.

Becomes one fourth.

Let the side of the square be $x.$

Then, area = (Side \times Side) $= (x \times x) = x^2$
If the sides are halved, new side $=\frac{\text{x}}{2}$
Now, new area $=\big(\frac{\text{x}}{2}\big)^{2}$
$=\frac{(\text{x})^{2}}{4}$
It is clearly visible that the area has become one-fourth of its previous value.

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MCQ 1601 Mark

Mark $(\checkmark)$ against the correct answer in the following:
The diameter of a wheel of a car is $70\ cm$. How much distance will it cover in making $50$ revolutions?

A
$350m$
✓
$110m$
C
$165m$
D
$220m$

Answer

Correct option: B.

$110m$

Circumference $=\pi \text{d}$
$=\frac{22}{7}\times 70$
$=220\text{cm}$
And distance in $50$ revolutions
$=\frac{22\times 50}{100}\text{m}$
$=110\text{m}$

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MCQ 1611 Mark

If the diagonal of a square is ${12}\sqrt{2}\text{cm}$ then the perimeter of square is .......

A
${24}\text{cm}$
B
${24}\sqrt{2}\text{cm}$
✓
${48}\text{cm}$
D
${48}\sqrt{2}\text{cm}$

Answer

Correct option: C.

${48}\text{cm}$

Perimeter of the square $(P) = 48$ units
Step - by - step explanation:
Let side ofasquare $= a$ units
Diagonal$(d) = 12$ and $8730 ; 2$ units $\times $ given
Now,
Area of square $\text{(A)} = \text{a}^{2} = \frac{\text{d}^{2}}{2}$
$\text{a}^2 = \frac{(12\sqrt{2})^2}{2}$
$\Rightarrow\text{a}^2 = \frac{12^2\times2}{2}$
$\Rightarrow\text{a}^2 {(12\text{ unit})}^2$
$\Rightarrow\text{a} = \sqrt{12}^2$
$\text{a} = {12}\text{ unit}$
$\text{perimeter of the square }(\text{p}) = {4}\text{r} $
$= {4}\times{12}\text{ unit}$
$\therefore\text{p} = {48} \text{ unit}$

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MCQ 1621 Mark

The perimeter of a rectangle whose length $(l)$ and breadth $(b)$ are given, is:

✓
$2(l + b)$
B
$2l + b$
C
$2l + 3b$
D
None of these

Answer

Correct option: A.

$2(l + b)$

Perimeter of a rectangle is the sum of all its four sides.
Since, two sides measure l and the other two sides measure b, Perimeter of a rectangle whose length $(l)$ and breadth $(b)$ are given, is $l + b + l + b = 2(l + b)$

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MCQ 1631 Mark

The area of a playground is $1600$ square metres. What is its perimeter?
$(I)$ It is a perfect square playground
$(II)$ It costs $Rs. 3200$ to put a fence around the play ground at the rate of $Rs. 20$ per metre

A
Statement $(I) ALONE$ is sufficient, but statement $(II) B$ alone is not sufficient
B
Statement $(II) ALONE$ is sufficient, but statement $(I)$ alone is not sufficient
C
$BOTH$ statements $TOGETHER$ are sufficient, but $NEITHER$ statement alone is sufficient
✓
$EACH$ statement $ALONE$ is sufficient

Answer

Correct option: D.

$EACH$ statement $ALONE$ is sufficient

From $(I) :$ We can find the side, area and perimeter ofsquare.From
$(II) :$ Since Perimeter $\times $ rate of fencing per metre = Total cost (in rupees)
each statement alone is sufficient.

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MCQ 1641 Mark

The total length of the closed figure is called .......

✓
perimeter
B
sum
C
area
D
total

Answer

Correct option: A.

perimeter

The total length of a closed figure is the sum of lengths of its boundaries which is also known as a perimeter.

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MCQ 1651 Mark

Mark the correct alternative in the following question:
The area of a square of side $14 \ cm$ is:

A
$49\ cm^2$
B
$156\ cm^2$
C
$56\ cm^2$
✓
$196\ cm^2$

Answer

Correct option: D.

$196\ cm^2$

The area of the square = (Side $\times $ Side)

$= 14 \times 14$
$= 196\ cm^2$

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MCQ 1661 Mark

If perimeter of a square is tripled, then area will be ........ of original area:

A
$4$ times
B
$\frac{1}{4}$ times
✓
$9$ times
D
$\frac{1}{9}$ times

Answer

Correct option: C.

$9$ times

$P = 4 \times S = 4SP_{new} = 4\times S′ = 4S′ P_{new} = 3P $
thus, $4S′ = 12SS = 3S A = S^2A = (S)^2A′ = (3S)^2A′$
$⟹A′ = 9A$

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MCQ 1671 Mark

In a rectangle, the difference between the sum of the adjacent sides and the diagonal is half of the longer side. what is the ratio of the shorter side to the longer side?

A
$\sqrt{3} : \sqrt{2}$
B
${1} : \sqrt{3}$
C
$2 : 5$
✓
$3 : 4$

Answer

Correct option: D.

$3 : 4$

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MCQ 1681 Mark

If the perimeter of a rectangle is p and its diagonal is d, the difference between the length and width of the rectangle is:

✓
$\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}$
B
$\frac{\sqrt{8\text{d}^{2}+\text{p}^{2}}}{2}$
C
$\frac{\sqrt{6\text{d}^{2}-\text{p}^{2}}}{2}$
D
$\frac{\sqrt{6\text{d}^{2}+\text{p}^{2}}}{2}$

Answer

Correct option: A.

$\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}$

Perimeter of the rectangle $= P2(l + b) = P \Rightarrow $
$1+\text{b}=\frac{\text{P}}{2}\rightarrow$
$(1)$ diagonal of the rectangle $ = \text{d}\sqrt{1^2+\text{b}^2}=\text{d}$
$\Rightarrow{1}^{2}+\text{b}^{2}=\text{d}^{2}$
$(1)^2 ⟹ d^2 + 2lb =$
$\frac{\text{p}^{2}}{4}$ $\Rightarrow 2lb =\frac{\text{p}^2 - 4\text{d}^2}{4}$
$⟹ l^2 + b^2− 2lb = d^2$
$=\frac{\text{p}^2 - 4\text{d}^2}{4}$
$\Rightarrow(1-\text{b})^{2}=$$=\frac{\text{8d}^2 - \text{pd}^2}{4}$
$\Rightarrow (1 - b)$
$\frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}$
$\therefore$ Difference between length and breadth $ = \frac{\sqrt{8\text{d}^{2}-\text{p}^{2}}}{2}$

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MCQ 1691 Mark

The area of a square field is $7744sq.$ meter. Find its perimeter:

A
$84m$
B
$176m$
✓
$352m$
D
$44m$

Answer

Correct option: C.

$352m$

We know that the area of square is $a^2$
$\Rightarrow 7744 = a^2$
$\Rightarrow\text{a} = \sqrt{7744}$
$\Rightarrow a = 88m$
We know that perimeter of square is $4a$
$\therefore$ perimeter $= 4 \times 88 = 352m$

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MCQ 1701 Mark

Calculate area of the figure made by joining $25$ unit squares:

A
$22sq$. unit
B
$23sq$. unit
C
$24sq$. unit
✓
$25sq$. unit

Answer

Correct option: D.

$25sq$. unit

Area of figure $= 25 \times 1 = 25sq$. unit

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MCQ 1711 Mark

The ratio of the length and breadth of a rectangle is $4 : 2.$ The area of the rectangle is $288\ cm^2$the perimeter of the rectangle will be:

A
$36\ cm$
✓
$72\ cm$
C
$70\ cm$
D
$60\ cm$

Answer

Correct option: B.

$72\ cm$

Let the length and breadth of the rectangle be $4xcm$ and $2xcm$ respectively.
$\therefore$ Area of the rectangle $= 8x^2$
$= 288$
$\Rightarrow x^2= 36$
$\Rightarrow x = 6$
$\therefore$ Length $= 24\ cm$
and Breadth $= 12\ cm$
$\therefore$ Perimeter of the rectangle $= 2(24 + 12)$
$= 72\ cm$

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MATHS M.C.Q. [1 Marks Each]