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Question
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`
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