Question
Draw a rectangle whose one side measures $8\ cm$ and the length of each of whose diagonals is $10\ cm$.
✓
Answer
Steps of construction:
$1.$ Draw a line segment $\text{AB} = 8\ cm$
$2.$ At $B$, draw a perpendicular $\text{BX}$
$3.$ With centre $A$ and radius $10\ cm$, draw an arc which intersects $\text{BX}$ at $C$.
$4.$ With centre $C$ and radius equal to $\text{AB}$ and with centre $A$ and radius equal to $\text{BC}$, draw arcs which intersect at $D$.
$5.$ Join $\text{AD, AC, CD}$ and $\text{BD}$.
Then $\text{ABCD}$ is the required rectangle.
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Locate the points:
$1. (1, 1), (1, 2), (1, 3), (1, 4)$
$2. (2, 1), (2, 2), (2, 3), (2, 4)$
$3. (1, 3), (2, 3), (3, 3), (4, 3)$
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$2. (2, 1), (2, 2), (2, 3), (2, 4)$
$3. (1, 3), (2, 3), (3, 3), (4, 3)$
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→Match each of the entries in Column $I$ with the appropriate entry in Column $II$
→|
S.No
|
Column $I$
|
S.No
|
Column II
|
|
$1.$
|
x and y vary inversely to each other
|
$A.$
|
$\frac{\text{x}}{\text{y}}=\text{constant}$
|
|
$2.$
|
Mathematical representation of inverse
variation of quantities $p$ and $q$
|
$B.$
|
$y$ will increase in proportion
|
|
$3.$
|
Mathematical representation of
direct variation of quantities
$m$ and $n$
|
$C.$
|
$xy$ = Constant
|
|
$4.$
|
When $x = 5, y = 2.5$ and when
$y = 5, x = 10$
|
$D.$
|
$\text{p} \propto\frac{1}{\text{q}}$
|
|
$5.$
|
When $x = 10 , y = 5$ and when
$x = 20, y = 2.5$
|
$E.$
|
$y$ will decrease in proportion
|
|
$6.$
|
x and y vary directly with each other
|
$F.$
|
$x$ and $y$ are directly proportional
|
|
$7.$
|
If x and y vary inversely then on decreasing x
|
$G.$
|
$\text{m }\alpha \text{ n}$
|
|
$8.$
|
If x and y vary directly then on decreasing
|
$H.$
|
$x$ and $y$ vary inversely
|
|
|
|
$I.$
|
$\text{p } \alpha \text{ q}$
|
|
|
|
$J.$
|
$\text{m }\alpha \frac{1}{\text{n}}$
|
Resolve each of the following quadratic trinomial into factor:
$7x - 6 - 2x^2$
→$7x - 6 - 2x^2$