# The Perimeter of a Triangle is 300 M. If Its Sides Are in the Ratio 3 : 5 : 7. Find the Area of the Triangle ? - Mathematics

The perimeter of a triangle is 300 m. If its sides are in the ratio 3 : 5 : 7. Find the area of the triangle ?

#### Solution

Given that
The perimeter of a triangle = 300 m
The sides of a triangle in the ratio 3 : 5 : 7
Let 3x, 5x, 7x be the sides of the triangle
Perimeter ⇒ 2s = a + b + c
⇒ 3x + 5x + 17x = 300
⇒ 15x = 300
⇒ x = 20m
The triangle sides are a = 3x
= 3 (20)m = 60 m
b = 5x = 5(20) m = 100m
c = 7x = 140 m

semi perimeter s = (a+b+c+)/2

=(300)/2m

=150m

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

=sqrt(150(150-60)(150-100)(150-140))

=sqrt(150xx10xx90xx50)

=sqrt(1500xx1500)     3 cm^2

∴Δ le Area = 1500 sqrt3 cm^2

Concept: Area of a Triangle by Heron's Formula
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Exercise 17.1 | Q 6 | Page 8

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