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