Question

The sides of a triangle are 39 cm, 42 cm and 45 cm. A parallelogram stands on the greatest side of the triangle and has the same area as that of the triangle. Find the height of the parallelogram.

Answer 1

In $△ABC$, by Heron's formula we have
$a=39cm,b=45cm$ and $c=42cm$
$\Rightarrow s=\frac{a+b+c}{2}=\frac{39+42+45}{2}=63cm$

$\therefore$ Area of $\Delta ABC=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{63(63-39)(63-42)(63-45)}$

$=\sqrt{63\times 24\times 21\times 18}$

$=756c{m}^2$
Given both the triangle and parallelogram have equal areas.

$A\left(\square BCED\right)=base\times height$

$\Rightarrow 45\times h=756c{m}^2\Rightarrow h=16.8cm$