Question

The area of a trapezium is 384cm2 . It's parallel sides are in the ratio 3:5 and the distance between them is 12cm. The longer of the parallel sides is A 24 cm
B 40cm
C 32 cm
D 36 cm

Answer 1

Step-by-step explanation:

Let the measures of the parallel sides be 3x and 5x respectively.

$\because \: Area \: of \: trapezium \\ = \frac{1}{2} \times (sum \: of \: \parallel \: sides) \times distance \: between \: them \\ \\ \therefore \: 384 = \frac{1}{2} \times (3x + 5x) \times 12 \\ \\ \therefore \: 384 =8x \times 6\\ \\ \therefore \: 384 =48x \\ \\ \therefore \: x = \frac{384}{48} \\ \\ \therefore \: x = 8 \\ \\ \implies \: \\3x = 3 \times 8 = 24 \: cm \\ \\ 5x = 5 \times 8 = 40 \: cm$

Thus, the longer of the parallel sides is 40 cm.

$\purple {{<strong> </strong>Hence, \: option \: B \: 40 \: cm \: is \: the \: correct \: answer.}}$