Question

The perimeter of a triangle field is 540 m and its sides are in ratio 25:17:12. Find the area of triangle.

Answer 1

Perimeter of triangle = a + b + c
540 = 25x + 17x + 12x
540 = 54x
x = 10
Then the sides are 250 m, 170m,120m
Area, using heron formula= ( s(s - a)(s - b)(s - c)
= √ 270×(270 - 250)×(270 - 170)×(270 - 120) sq. m
= √ 270×20×100×150 sq. m
= √ 81000000 sq.m
= 9000 sq.m. ans...

hope this will help...

Answer 2

Perimeter of Triangle is 540 m.

Ratio of sides is 25:17:12

Let the sides be 25x , 17x and 12x respectively.

So, according to Question -

25x + 17x + 12x = 540

or, 54x = 540

or, x = 540/54

or, x = 10

Sides -

25x = 25×10 = 250m

17x = 17×10 = 170m

12x = 12×10 = 120m

Semi-perimeter (s) = 540/2 = 270m

Area of triangle using heron's formula =

√s(s-a)(s-b)(s-c)

where, a,b and c are sides of triangle.

√270(270-250)(270-170)(270-120)

= √270(20)(100)(150)

= √2×3×3×3×5×2×2×5×2×2×5×5×2×3×5×5

= 2×2×2×3×3×5×5×5

= 9000m²

Answer) Area of Triangle is 9000 m².