The Perimeter of a Triangullar Field is 144 M and the Ratio of the Sides is 3 : 4 : 5. Find the Area of the Field. - Mathematics

The perimeter of a triangullar field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.

Solution

The area of a triangle having sides aband s as semi-perimeter is given by,

A = sqrt(s(s-a)(s-b)(s-c)), where,

s = (a+b+c)/2

It is given the sides of a triangular field are in the ratio 3:4:5 and perimeter=144 m

Therefore, abc = 3:4:5

We will assume the sides of triangular field as

a= 3x : b = 4x ; c = 5x

2s = 144

s= 144/2

s= 72

72= (3x+4x+5x)/2

72×2= 12x

  x = 144/12

x = 12

Substituting the value of in, we get sides of the triangle as

a = 3x = 3 × 12

a = 36 m

b = 4x = 4 × 12

b = 48 m

c = 5x = 5 × 12

c = 60 m

Area of a triangular field, say having sides aand as semi-perimeter is given by

a = 36 m ; b = 48 m ; c = 60 m

s = 72 m

A = sqrt( 72(72-36) (72-48)(72-60)

A=sqrt(72(36)(24)(12))

A= sqrt(746496)

A = 864 m2

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RD Sharma Mathematics for Class 9
Chapter 17 Heron’s Formula
Q 6 | Page 24