Question

A trapezium with its parallel sides is in the ratio 16: 5 is cut from a rectangular whose sides measure 63 m and 5 m respectively. The area of the trapezium is $\frac{4}{15}$ of the rectangle. Find the difference between the lengths of the parallel sides of the trapezium.

• A. 13.6 m
• B. 18.4 m
• C. 17.6 m​
• D. None of these

Answer 1

The correct option is C

17.6 m​

Let the length of the rectangle = 63 m

Width of the rectangle = 5 m

Area of the rectangle = 63 $\times$ 5 = 315 $m^2$

Area of the trapezium = $\frac{4}{15}$ (Area of the rectangle)

= $\frac{4}{15}$ $\times$ 315 = 84 $m^2$

Height of the trapezium = $\left(\frac{4}{15}\right)$ $\left(sumofparallelsides\right)$ $\times$ height

$\Rightarrow$ 84 = $\frac{1}{2}$ (16 x + 5x ) $\times$ 5

$\Rightarrow$ x = $\frac{8}{5}$

Therefore, 16x = $16\times \frac{8}{5}$ = 25.6 m and 5x = $5\times \frac{8}{5}$ = 8 m.

So, the difference between the lengths of the parallel sides of the trapezium​ = 25.6 m - 8 m = 17.6 m.