Question

The length of the parallel sides of a trapezium are in the ratio 3: 2 and the distance between them is 10 cm. If the area of the trapezium is 325 cm², find the length of the parallel sides.

• A. 20cm , 40cm
• B. 26 cm , 39 cm
• C. 22 cm , 36 cm
• D. 19 cm , 41 cm

Answer 1

The correct option is B

26 cm , 39 cm

Since the parallel sides are in the ratio 3:2 therefore, $a=3x$ and $b=2x$
Now, area of the trapezium = $\frac{1}{2}(2x+3x)\times 10$
$=(2x+3x)\times 10=325\times 2=650$

5x=$\frac{650}{10}$ $\Rightarrow$ $5x=65$ $\Rightarrow$ $x=13$
$a=2\times x=2\times 13=26$
$b=3\times x=3\times 13=39$
Hence, the parallel sides are 26 cm and 39 cm.