Question

If the perimeter of an isosceles triangle is $11$ cm and the base is $5$ cm, its area is given by

• A. $\frac{15}{2}c{m}^2$
• B. $\frac{83}{20}c{m}^2$
• C. $\frac{45}{15}c{m}^2$
• D. $\frac{52}{12}c{m}^2$

Answer 1

Answer: (B)

$\frac{83}{20}c{m}^2$

$AB+BC+CA=11cm$

$BC=5cm$

$\Rightarrow AB=AC=3cm$

Now, using Pythagoras theorem, we get

$h^2=(AB{)}^2-(BD{)}^2$

$=3^2-(2.5{)}^2$

$=2.75{cm}^2$
$\Rightarrow h=1.66cm$

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

$=\frac{5\left(1.66\right)}{2}$

$=\frac{83}{20}{cm}^2$