Question

The perimeter of a triangle 120cm and it`s sides are in the ratio 5:12:13.Find the area of the triangle?

Answer 1

120cm = perimeter ratio of sides = 5x, 12x, 13x. 5x + 12x +13x = 120cm 20x =120cm x= 120/20 x= 6cm 5x= 6 x 5 =30 12x= 6 x 12= 72 15x= 6x15=90 therefore the sides are 30cm, 72cm, 90cm.

Answer 2

let the sides be 5x, 12x &13x. So,

5x+12x+13x=120 (given)

40x=120

x=120/40

x=3

∴,

5x=5 X 3=15

12x= 12 X 3=36

13x= 13 X 3=39

now,

Area⇒ s=a+b+c/2

=15+36+39/2

=120/2

=60

√s(s-a)(s-b)(s-c)=area of triangle

=√60(60-15)(60-36)(60-39)

=√60(45)(24)(21)

=√2×3×2×5××3×3×2×2×3×2×7×3

=2×2×3×3×5×2√7×3

=360√21cm²