Question

The perimeter of a triangle field is $144m$ and ratio of the sides is $3:4:5$. Then the area of the field is

• A. $864$ sq m
• B. $764$ sq m
• C. $854$ sq m
• D. $754$ sq m

Answer 1

The correct option is A $864$ sq m

Let the sides of the triangle be $3a,4a,5a$.
Perimeter of the triangle $=3a+4a+5a$

$=12a$
Given, perimeter of the triangle $=144m$

$\Rightarrow 12a=144m$

$a=12m$
So, the sides of the triangle are

$3a=36m,4a=48m,5a=60m$.

Area of triangle with sides $a,b$ and $c$ is given as is $\sqrt{s(s-a)(s-b)(s-c)}$.

Where

$s=\frac{a+b+c}{2}$

For triangle with sides $36m,48mand60m,$

$s=\frac{36+48+60}{2}=72m$
Thus

$A=\sqrt{72(72-36)(72-48)(72-60)}=\sqrt{72\times 36\times 24\times 12}$

$=\sqrt{36\times 2\times 36\times 12\times 2\times 12}$

$=36\times 12\times 2=864m^2$