Question

If the parallel sides of a trapezium are in the ratio 4:5 and its height is 6 cm and its area is 54 $c{m}^2$, then find the lengths of parallel sides.

• A. 4 cm, 5 cm
• B. 8 cm, 10 cm
• C. 12 cm, 15 cm
• D. 16 cm, 20 cm

Answer 1

The correct option is B 8 cm, 10 cm

Let the parallel sides be 4y and 5y.
Area of trapezium
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
54 = $\frac{1}{2}$$\times$(5y+4y)$\times$6
54 = 9y$\times$3 = 27y
y = $\frac{54}{27}$ = 2
Hence, parallel sides are
4y = 4$\times$2 = 8 cm,
5y = 5$\times$2 = 10 cm.