Question

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are $26cm,28cm$ and $30cm$, and the parallelogram stands on the base $28cm$, then the height of the parallelogram is

• A. $42cm$
• B. $12cm$
• C. $24cm$
• D. $21cm$

Answer 1

The correct option is B $12cm$

Area of the parallelogram and triangle are equal.

Length of the sides of the triangle are $26$ cm$,28$ cm and $30$ cm.

Perimeter of the triangle $=26+28+30=84$ cm

Semi perimeter of the triangle$=\frac{84}{2}=42$ cm

Using heron's formula,

$A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{42(42-26)(42-28)(42-30)}=\sqrt{42\times 16\times 14\times 12}=\sqrt{112896}=336$ cm${}^2$

Let height of parallelogram be $h$.

Area of parallelogram = Area of triangle

$28\times h=336$

$h=\frac{336}{28}=12$ cm

Hence, the height of the parallelogram is $12$ cm.