Question

The perimeter of a triangle is $540$ m and its sides are in the ratio $12:25:17.$ Find the area of the triangle.

• A. $5,000m^2$
• B. $6,000m^2$
• C. $9,000m^2$
• D. $8,000m^2$

Answer 1

The correct option is C $9,000m^2$

Let the sides of the triangle be $12a,25a,17a$.
We know that perimeter of the triangle $=$ Sum of all sides $

$\Rightarrow 12a+25a+17a=54a$

Given, perimeter of the triangle $=540m$
$\Rightarrow 54a=540m$
$a=10m$
So, the lengths of the sides of triangle are

$12a=120m$

$25a=250m$

$17a=170m$

We can use Heron's formula to get the area of triangle

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

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

For triangle with sides 120 m, 250 m and 170 m,

$s=\frac{120+250+170}{2}$

$=270m$
Substituting the sides 120 m, 250 m and 170 m in the Heron's formula, we get

$\sqrt{270(270-120)(270-250)(270-170)}$

$=\sqrt{270\times 150\times 20\times 100}$

$=\sqrt{9\times 30\times 30\times 5\times 20\times 20\times 5}$

$=3\times 30\times 5\times 20$

$=9000m^2$