Question

the side of a triangle are in the ratio 11 :19:24 and its perimeter is 540 cm find the area of triangle
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Answer 1

Answer:

Step-by-step explanation

peremeter = sum of all sides

P=540

S1+s2+s3=540

11 x +19 +24x=540

54x=540

X=10

S1=110

S2=190

S3=249

Answer 2

The area of triangle is 10182.34 sq. cm  .

Explanation:

Given : The side of a triangle are in the ratio 11 :19:24.

Let the sides of triangle are 11x , 19 x , 24 x

Perimeter = 11x +19x+24x=54x

Since its perimeter is 540

⇒ 54 x = 540 cm

⇒ x= 10 cm

Then, the sides of triangle is 110 cm , 190 cm , 240 cm.

Semi perimeter: $s=\dfrac{540}{2}=270$

By Hereon's formula

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

Therefore , Area of given triangle = $\sqrt{270(270-110)(270-190)(270-240)}$

$\approx10182.34\ cm^2$

Hence, the area of triangle is 10182.34 sq. cm  .

# Learn more :

The sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm find its area

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