Question

In the given figure, AB || CD, AB = 7 cm, BD = 25 cm and CD = 17 cm. Find the length of side BC(cm).

Answer 1

Given: $AB\parallel CD$
Construction: Draw a perpendicular on CD from B, meting CD at E
Thus, BE = AD
Now, In $△ABD$,
$B{D}^2=A{D}^2+A{B}^2$
${25}^2=A{D}^2+7^2$
$AD=24$ cm
thus, $BE=AD=24$ cm
and $CE=CD-AB=17-7=10$ cm
Now, In $△BCE$
$B{C}^2=B{E}^2+C{E}^2$
$B{C}^2={24}^2+{10}^2$
$B{C}^2=676$
$BC=26$ cm