Question

The perimeter of a triangle is 450 m and its side are in the ratio 12: 5: 13. Find the area of the triangle.

Answer 1

Let the sides of the triangle be
a = 12x
b = 5x
c = 13x

Given that the perimeter = 450 m
⇒ 12x + 5x + 13x = 450
⇒ 30x = 450
⇒ x = 15

Hence, the sides of a triangle are
a = 12x = 12(15) = 180 m
b = 5x = 5(15) = 75 m
c = 13x = 13(15) = 195 m

Now,
semi-permeter of a triangle,
s = `[a + b + c]/[2] = (180 + 75 + 195)/(2) = (450)/(2 ) = 225"m"`

∴ Area of triangle = `sqrt( s (s - a )( s - b ) (s -c )`

= `sqrt( 225 ( 225 - 180 )( 225 - 75 ) ( 225 -195 )`

= `sqrt( 225 xx 45 xx 150 xx 30 )`

= `sqrt( 15 xx 15 xx 9 xx 5 xx 25 xx 6 xx 5 xx 6)`

= `sqrt( 15 xx 15 xx 3 xx 3 xx 25 xx 25 xx 6 xx 6)`

= 15 x 3 x 25 x 6

= 6750 m²