Sides of a Triangle Are in the Ratio of 12: 17: 25 and Its Perimeter is 540 cm. Find Its Area. - Mathematics

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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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Solution

Let the common ratio between the sides of the given triangle be x.

Therefore, the side of the triangle will be 12x, 17x, and 25x.

Perimeter of this triangle = 540 cm

12x + 17x + 25x = 540 cm

54x = 540 cm

x = 10 cm

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

`s="perimeter of triangle"/2=540/2=270cm`

By Heron's formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

                          `=[sqrt(270(270-120)(270-170)(270-250))]cm^2`

                          `=[sqrt(270xx150xx100xx20)]cm^2`

                           = 9000 cm2

Therefore, the area of this triangle is 9000 cm2.

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Chapter 12: Heron's Formula - Exercise 12.1 [Page 203]

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NCERT Mathematics Class 9
Chapter 12 Heron's Formula
Exercise 12.1 | Q 5 | Page 203

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