Question

In `square` ABCD side AB || side DC, seg AE ⊥ seg DC. If l(AB) = 9 cm, l(AE) = 10 cm, A(`square` ABCD) = 115 cm², find l(DC).

Answer 1

Given, side AB || side DC.

l(AB) = 9 cm, l(AE) = 10 cm,

A(ABCD) = 115 cm²

∴ ABCD is a trapezium.

Area of a trapezium

= `(1/2) xx "sum of lengths of parallel sides" xx "height"`

∴ A(ABCD) = `(1/2) xx (l("AB") + l("DC") xx l("AE"))`

∴ `115 = (1/2) xx (9 + l("DC")) xx 10`

∴ `(115 xx 2)/10 = 9 + l("DC")`

∴ 23 = 9 + l(DC)

∴ l(DC) = 23 – 9

∴ l(DC) = 14 cm