Question

The perimeter of a triangle is 170 feet and the sides are in the ratio of 25:14:12. Find the area of the triangle.

Answer 1

Step-by-step explanation:

let the sides be 25x,14x,12x

25x+14x+12x=170

51x=170

x=10÷3

sides are:250÷3,140÷3,120÷3

Answer 2

Answer:

$494.34\ feet^2$

Step-by-step explanation:

Given,

ratio of sides of triangle = 25:14:12

Let's consider the sides of triangle are 25x, 14x and 12x

Perimeter of triangle = 170 feet

=> 25x + 14x + 12x = 170

=> 51x = 170

$=>\ x\ =\ \dfrac{10}{3}$

Hence, sides of triangle are

$a\ =\ 25\times \dfrac{10}{3}$

      $=\ \dfrac{250}{3}\ feet$

$b\ =\ 14\times \dfrac{10}{3}$

      $=\dfrac{140}{3}\ feet$

$c\ =\ 12\times \dfrac{10}{3}$

       $=\ 40\ feet$

Semi-perimeter of triangle,

       $s\ =\ \dfrac{perimeter}{2}$

            $=\ \dfrac{170}{2}\ feet$

             = 85 feet

According to Heron's formula, area of triangle is given by

$A\ =\ \sqrt{s(s-a)(s-b)(s-c)}$

   $=\ \sqrt{85(85-\dfrac{250}{3})(85-\dfrac{140}{3})(85-40)}$

    $=\ 494.34\ feet^2$

Hence, the area of triangle will be $494.34\ feet^2$