Question

$ABCD$ is a parallelogram, $AE$ is perpendicular to $DC$, If $DC=20cm$, $AD=5cm$ and the area of the parallelogram is $40c{m}^2$. Find $DE$.

Answer 1

Area $=CD\times AE=AE\times 20=40㎠$

So, $AE=2㎝$

In $△AED$, using Pythagoras, we get

${AE}^2+{ED}^2={AD}^2$

So, $2^2+{ED}^2=5^2$

${ED}^2=5^2-2^2$

$ED=\sqrt{25-4}=\sqrt{21}㎝$