The area of a small rectangular plot is 84 m^2. If the difference… - Vidyadip

Question

The area of a small rectangular plot is $84\ m^2.$ If the difference between its length and the breadth is $5 \ m$ ; find its perimeter.

✓

Answer

Area of a rectangular plot $= 84\ m^2$
Let breadth $= x\ m$
Then length $= (x + 5)\ m$
Area $= l \times b$
$x(x + 5) = 84$
$x^2 + 5x – 84 = 0$
$=> x^2+ 12x – 7x – 84 = 0$
$=> x(x + 12) – 7(x + 12) = 0$
$=> (x + 12) (x – 7) = 0$
Either $x + 12 = 0$, then $x = -12$ which is not possible being negative
or $x – 7 = 0,$ then $x = 7$
Length $= x + 5 = 7 + 5 = 12m$
and breadth $= x = 7 m$
Perimeter $= 2(l + b) = 2(12+ 7) = 2 \times 19\ m = 38\ m$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Area of a Trapezium and a Polygon→Area of a Trapezium and a Polygon — all question types→MATHS STD 8 question papers→ICSE Board STD 8 question papers→ICSE Board question paper generator→

Similar questions

The weights (in kg) of 30 students are given below :
$
\begin{array}{l}
48,55,30,43,41,36,48,37,34,38,46,42,38,52,37 \\
34,40,42,50,37,35,46,42,45,43,37,39,45,48,46
\end{array}
$
Form the grouped frequency table by taking class-intervals
$30-35,35-40,40-45,45-50$, $50-55$.

Solve the following equation : $3 a-\frac{1}{5}=\frac{a}{5}+5 \frac{2}{5}$

The length, breadth, and height of a cuboid are in the ratio $5 : 3: 2$. If its volume is $240 \ cm^3;$ find its dimensions. Also, find the total surface area of the cuboid.

The cost price of an article is $\frac{4}{5}$ times of its selling price. Find the loss or the gain as a percent.

The total surface area of a cylinder is $6512\ cm^2$ and the circumference of its bases is $88\ cm.$ Find : $(i)$ its radius $(ii)$ its volume

What sum of money lent at $6.5\%$ per annum will produce the same interest in $4$ years as $Rs.7500$ produce in $6$ years at $5\%$ per annum?

For each set of rational number, given below, verify the associative property of addition of rational number: $(i)$ $-1, \frac{5}{6}$ and $\frac{-2}{3}$

Thirty articles are bought at $Rs. 450$ each. If one$-$third of these articles be sold at a $6\%$ loss; at what price must each of the remaining articles be sold in order to make a profit of $10\%$ on the whole?

Divide : $\left(6 x^5+4 x^4-3 x^3-1\right)$ by $\left(3 x^2-x+1\right)$

Evaluate : $(a+1) (a-1) (a^2+1)$