Question

ABCD is a trapezium of area 91 cm2. cd is parallel to ab and cd is longer than ab by 8cm. if the distance between ab and cd is 7cm, find ab and cd

Answer 1

$let \: ab = x \: cm \\ cd = (x + 8)cm \\ since \\ \\ ar(abcd) = \frac{1}{2} \times (ab + cd) \times distance\\ 91cm {}^{2} = \frac{1}{2} \times (x + x + 8) \times 7 \\ \frac{91}{ 7} = x + 4 \\ x = 9cm \\ ab = 9cm \\ cd = 9 + 8 = 17cm$