Question

The sides of a triangle are in the ratio $3:4:5$. If its perimeter is $36cm$, area of the triangle is:

• A. $57c{m}^2$
• B. $54c{m}^2$
• C. $56.5c{m}^2$
• D. $Noneofthese$

Answer 1

Answer: (B)

$54c{m}^2$

Given;-

perimeter$=36$

let the ratio be $x$

therefore,

$\Rightarrow AB+BC+CA=36$

$\Rightarrow 3x+4x+5x=36$

$\Rightarrow 12x=36$

$\begin{array}{c}\Rightarrow x=\frac{36}{12}\\ \Rightarrow x=3\end{array}$

Now, putting the value of $x$

$AB=3x=9cm$

$BC=4x=12cm$

$AC=5x=15cm$

On using Pythagoras theorem

$\begin{array}{c}A{C}^2=A{B}^2+B{C}^2\\ ={\left(9\right)}^2+{\left(12\right)}^2\\ =81+144\\ A{C}^2=225\\ AC=15cm\end{array}$

$\Delta ABC$ is right angled triangle $\angle B$ is right angle.

Area of $\begin{array}{c}\Delta ABC=\frac{1}{2}AB\times BC\\ =\frac{1}{2}\times 9\times 12\\ =54c{m}^2\end{array}$

hence,

Area of triangle is $54c{m}^2$