Question

Parallel sides of a trapezium are in the ratio 2:3 and if its height is half the length of smaller parallel side, then find the lengths of parallel sides if area of the trapezium is 40 $c{m}^2.$

• A. 4 cm, 6 cm
• B. 6 cm, 9 cm
• C. 8 cm, 12 cm
• D. 10 cm, 15 cm

Answer 1

The correct option is C 8 cm, 12 cm

Let lenght of the larger parallel side's length be 3x and the length of the smaller parallel side be 2x
Height = $\frac{2x}{2}$ = x
Area of trapezium
= $\frac{1}{2}$$\times$(sum of parallel sides)$\times$height
40 = $\frac{1}{2}$$\times$(sum of parallel sides)$\times$height
40 = $\frac{1}{2}$$\times$(2x+3x)$\times$x
40 = $\frac{1}{2}$$\times$(5x)$\times$x
$\frac{40\times 2}{5}$ = 16 = $x^2$
x = $\sqrt{1}6$ = 4
Length of the larger parallel side = 3y
= 3(4)= 12 cm
Length of the smaller parallel side = 2y
= 2(4)= 8 cm