# The Perimeter of a Triangular Field is 540 M and Its Sides Are in the Ratio 25 : 17 : 12. Find the Area of the Triangle ? - Mathematics

The perimeter of a triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the triangle ?

#### Solution

The sides of a triangle are in the ratio 25 : 17 : 12

Let the sides of a triangle are a = 25x, b = 17 x and c = 12x say.
Perimeter = 25 = a + b + c = 540 cm
⇒ 25x + 17x + 12x = 540 cm
⇒ 54x = 540cm

⇒ x = 540/54
⇒ x = 10 𝑐𝑚
∴ The sides of a triangle are a = 250 cm, b = 170 cm and c = 120 cm

Now, Semi perimeter s =(a+b+c)/2

=(540)/2=270cm

∴The aera of the triangle =sqrt(s(s-a)(s-b)(s-c))

=sqrt(270(270-250)(270-170)(270-120))

=sqrt(27(20)(100)(150))

sqrt((9000)(9000))

9000 cm^2\

The aera of triangle = 900cm^2

Concept: Area of a Triangle
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.1 | Q 5 | Page 8
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