Math, asked by eshan63, 11 months ago

30.
The sides of a triangle are in the ration 11:19:24 and its perimeter is
540cm. Find the area of the triangle

Answers

Answered by bhagyashreechowdhury
0

The area of the triangle is 10182.33 cm².

Step-by-step explanation:

The ratio of the sides of the triangle are = 11:19:24

So, let the sides of the triangle be “11x”, “19x” and “24x”.

The perimeter of the triangle = 540 cm

We know that,

The perimeter of the triangle = Sum of all sides = 11x + 19x + 24x = 54x.

∴ 54x = 540

x = 10 cm

So, the sides of the triangle are:  

11x = 11 * 10 = 110 cm

19x = 19 * 10 = 190 cm

24x = 24 * 10 = 240 cm

Now,  

Semi-Perimeter, s = [Perimeter of the triangle]/2 = 540/2 = 270 cm

Using Heron’s Formula, we get

Area of the triangle is,

=  √[s(s-a)(s-b)(s-c)] ……. Where a, b & c are the sides of the triangle

= √[270(270-110)(270-190)(270-240)]

= √[270 * 160 * 80 * 30]

= √[103680000]

= 101823.33 cm²

Thus, the area of the triangle is 101823.33 cm².

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