Question

The longer side of a parallelogram is 54$cm$ and the corresponding altitude is 16$cm$. If the altitude corresponding to the shorter side is $24cm,$ find the length of the shorter side.

Answer 1

Let $ABCD$ is a parallelogram with the longer side $AB=54cm$ and corresponding altitude $AE=16cm$.

The shorter side is $BC$ and the corresponding altitude is $CF=24cm$.

We know that area of a parallelogram $=$ base $\times$ height.

We have two altitudes and two corresponding bases.

By equating them we get,

$\frac{1}{2}\times BC\times CF=\frac{1}{2}\times AB\times AE$

On simplifying, we get

$BC\times CF=AB\times AE$

$\Rightarrow BC\times 24=54\times 16$

$\Rightarrow BC=\frac{54\times 16}{24}$

$\Rightarrow BC=36cm$

Hence, the length of the shorter side $BC=AD=36cm$.