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 = 30 , b = 26
• B. a = 20 , b = 40
• C. a = 26 , b = 39
• D. a = 40 , b = 20

Answer 1

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

Since the parallel sides are in the ratio 3:2 therefore, $a=3x$ and $b=2x$.
Now, area of the trapezium,
$325=\frac{1}{2}(2x+3x)\times 10$
$\Rightarrow (2x+3x)\times 10=650$
$\Rightarrow 5x=65$
$\Rightarrow x=13$
$\therefore a=2\times x=2\times 13=26$
$\therefore b=3\times x=3\times 13=39$
Hence, the parallel sides are 26 cm and 39 cm.