Question

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

Answer 1

Solution:-

Given triangle and parallelogram in some base

Area of triangle $=\sqrt{S(S-a)(S-b)(S-c)}$

$S=\frac{26+30+28}{2}=\frac{84}{2}=42m$

Area $=\sqrt{42(42-26)(42-28)(42-30)}$

$=\sqrt{42\times 16\times 14\times 12}$

$=336c{m}^2$

Now Area of Parallelogram $=base\times height$$=28\times height$

Area $=336c{m}^2$

$\Rightarrow 28\times height=336c{m}^2$

$\Rightarrow height=\frac{1}{28}\times 336=12cm$