Question

If the perimeter of an isosceles triangle is $11$ cm and its base is $5$ cm, its area is $\frac{5}{4}\sqrt{11}$ cm${}^2$. State true of false and give reason.

Answer 1

REF.IMAGE

$P=x+x+5=11cm$

$2x+5=11cm$

$2x=6cm\Rightarrow x=3cm$

Area = $\frac{1}{2}\times h\times 5$

$h=\sqrt{3^2-(5/2{)}^2}=\sqrt{9-25/4}=\sqrt{11/4}$

Area = $\frac{1}{2}\times \sqrt{\frac{11}{4}}\times 5$ = $\frac{5}{4}\sqrt{11}c{m}^2$

$\therefore True$