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. a = 20 , b = 40
• B. a = 26 , b = 39
• C. a = 22 , b = 36
• D. a = 19 , b = 41

Answer 1

The correct option is B a = 26 , b = 39

Given the parallel sides are in the ratio 3:2
Let the length of the two parallel sides to be 3x and 2x.
Area of the trapezium = $\frac{1}{2}\left(sumoftheparallelsides\right)\times distancebetweentheparallelsides$ =
$\frac{1}{2}(2x+3x)\times 10=325$

$\Rightarrow x=13$.
Hence,
$a=2\times x=2\times 13=26$ and
$b=3\times x=3\times 13=39$
Hence, the length of the parallel sides are 26 cm and 39 cm.