Question

Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.​

Answer 1

Answer:

let the sides of triangle be 12x, 17x, 25x

Perimeter = 12x + 17x + 25x

540 = 54x

540/54 = x

x = 10

Therefore, 12x = 12 × 10 = 120

17x = 17 × 10 = 170

25x = 25 × 10 = 250

Semiperimeter = 120+170+250/2

= 540/2 = 270cm

Area of ∆ = √s(s-a)(s-b)(s-c)

= √ 270(270-120) (270-170) (270-250)

= √ 270 × 150 × 100 × 20

= √ 3×9×10 × 3×5×10 × 10×10 × 4×5

= 3×3×10×10×2×5

= 9000cm²

Area of ∆ = 9000cm²

Answer 2

Step-by-step explanation:

Let side be x

Side A=12x

Side B=17x

Side c=25x

Perimeter of triangle = 540cm

=12x+17x+25x = 540cm

=54x =540cm

=x=540/54 =10 cm

Side A =12x = 12×10=120

Side B = 17x= 17×10=170

Side C = =25x=25×10=250

Semi perimeter = a+b+c/2

=120+170+250/2

=540/2 = 270

Area of triangle = Square root of s(s-a) (s-b) (s-c)

=Square root of 270(270-120) (270-170)(270-250)

=Square root of 270×150×100×20

=9000cm2

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