Question

In the adjoining figure, the area of the right angled triangle is $54{\text{cm}}^2$. If one of its legs is $12\text{cm}$ long, find its perimeter.

Answer 1

In the given diagram,

Area of right-angled triangle $=54{\text{cm}}^2$
Length of one leg $AB=12\text{cm}$

Area = $\frac{1}{2}\times$ base $\times$ height
$54=\frac{1}{2}\times$ base $\times 12$

base $=9\text{cm}$

Now,

${AC}^2={AB}^2+{BC}^2$ (Pythagoras Theorem)
$\begin{array}{c}={12}^2+9^2=144+81=225=(15{)}^2\\ AC=15cm\\ \text{Perimeter}=AB+BC+AC=12+9+15=36cm\end{array}$