The area of a trapezium is 475 cm² and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.

Let PQRS be the given trapezium,

Given PQ = 19cm

Let RQ be x cm

Then, PS = (x + 4)cm

We draw Perpendicular from R on PS which will also be parallel to PQ.

Now, PQRT is a rectangle,

Area(PQRT) = PQ × QR

⇒ Area(PQRT) = 19x

Now,

PS = PT + TS

⇒ (x + 4) = x + TS (As PT = QR = x cm)

⇒ TS = 4cm

Area(ΔRST) = 1/2 × RT × ST

⇒ Area(ΔRST) = 1/2 × 19 × 4 = 38cm² (As RT = PQ = 19cm)

Area(PQRS) = Area(PQRT) + Area(ΔRST)

⇒ 475 = 19x + 38

⇒ 19x = 475 -38

⇒ 19x = 437

⇒ x = 23 cm

(x + 4) = 23 + 4 = 27cm

∴ Lengths of parallel sides is 23cm and 27cm.