Question

Question 3
Write True or False and justify your answer:

The area of the isosceles triangle is $\frac{5}{4}\sqrt{11}c{m}^2$ if the perimeter is 11cm and the base is 5cm.

Answer 1

True
Let equal sides of an isosceles triangle be b.
$\therefore$ Perimeter of a triangle, 2s = b + b + 5 $[\because 2s=a+b+c]$
$\therefore$ 11 = 2b + 5
$\Rightarrow 2b=11-5\Rightarrow 2b=6$
$\Rightarrow b=\frac{6}{2}=3m$
We know that, area of an isosceles triangle
$=\frac{a}{4}\sqrt{4b^2-a^2}$
Here, sides of triangle are a = 5cm and b = 3cm
$\therefore$ Area fo an isosceles triangle $=\frac{5\sqrt{4(3{)}^2-(5{)}^2}}{4}$
$=\frac{5\sqrt{4\times 9-25}}{4}$
$=5\frac{\sqrt{36-25}}{4}$
$=\frac{5\sqrt{11}}{4}c{m}^2$