Question

The sides of a rectangle are in the ratio 2 : 3 and its perimeter is 20 cm. Draw the rectangle.

Answer 1

Perimeter of a rectangle = 20 cm
Ratio in the sides = 2 : 3

Let breadth (l) = 2x
The length (b) = 3x
$\therefore$ Perimeter = 2(l+b)
$\Rightarrow 20=2(2x+3x)\Rightarrow 4x+6x=20\Rightarrow 10x=20\Rightarrow x=\frac{20}{10}=2$
$\therefore$ Length = $3x=2\times 2=6$
and breadth = $2x=2\times 2=4cm$
Steps of construction:
(i) Draw a line segment AB=6 cm
(ii) At A and B draw perpendicular AX and BY.
(iii) Cut off from AX and BY, AC = BC = 4 cm
(iv) Join CD.
Then ABCD is the required rectangle.