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

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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 ?

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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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Chapter 17: Heron’s Formula - Exercise 17.1 [Page 8]

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

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