Question

side of triangle are in the ratio of 11:12:15 and its perimeter is 3800.find its area .by under using herons formula​

Answer 1

$\huge{\blue{\boxed{\mathbb{\orange{ANSWER:-}}}}}$

Let the ratio of the sides of the triangles be 11x, 12x, 15x respectively.

Given:-

Sides of the triangles in ratio:- 11x,12x,15x

Perimeter of the triangle:- 3800cm

To find:-

Area of the triangle using Heron's formula

Solution:-

We know that,

Perimeter of the triangle= side1+side2+side3

According to the Question,

$\tt{3800=11x+12x+15x}$

$\implies \tt{3800=38x}$

$\implies \tt{x = \dfrac{\cancel{3800}}{\cancel{38}}}$

${\boxed{\tt{x=100}}}$

$\tt{11x = 11(100) = 1100}$

$\tt{12x = 12(100) = 1200}$

$\tt{15x = 15(100) = 1500}$

Area of the triangle using Heron's formula:-

$\tt {p= \dfrac{side1+side2+side3}{2}}$

$\tt \sqrt{p(p-side1)(p-side2)(p-side3)}$

$\tt {p= \dfrac{1100+1200+1500}{2}}$

$\tt {p= 1900}$

$\implies \tt \sqrt{1900(1900-1100)(1900-1200)(1900-1500)}$

$\implies \tt \sqrt{1900(800)(700)(400)}$

$\implies \tt {6,52,380.25}$

Area of Triangle= 6,52,380.25cm²

Hope it helps!