Question

The base of an isosceles triangle measures $24$ cm and its area is $192{\text{cm}}^2$. Find its perimeter.

• A. $60$ cm
• B. $64$ cm
• C. $72$ cm
• D. $84$ cm

Answer 1

The correct option is B $64$ cm

$A=\frac{bh}{2}\Rightarrow h=\frac{2A}{b}$

$a=\sqrt{h^2+\frac{b^2}{4}}$

$P=2a+b$

Using all the above equations, we get,

$P=2\sqrt{h^2+\frac{b^2}{4}}+b$

$\Rightarrow P=2\sqrt{{\left(\frac{2A}{b}\right)}^2+\frac{b^2}{4}}+b$

$\Rightarrow P=2\sqrt{{\left(\frac{2\times 192}{24}\right)}^2+\frac{{24}^2}{4}}+24$

$\Rightarrow P=64$