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.


3
1