Question

Find the area of a triangle whose sides are in the ratio 5:12:13 and whose perimeter is 36cm.

Answer 1

Perimeter P of the triangle = P = 36cm
Ratio of the sides = 5:12:13
Let the constant of proportionality be k
⇒ 5k + 12k + 13k = 36
⇒ 30k = 36

⇒ k = `(36)/(30)`
= 1.2
∴ the sides are: 5 x 1.2, 12 x 1.2 and 13 x 1.2
i.e. 6cm, 14.4cm and 15.6cm
We know that, Area of a Triangle whose sides are a, b, and c and semiperimeter is s is given by `sqrt("s"("s" - "a")("s" - "b")("s" - "c")); "s" = ("a" + "b" + "c")/(2)`

For a triangle whose sides are 6cm, 2.4cm and 15.6cm
i.e. a = 6 b = 14.4cm and c = 15.6, s = `(36)/(2)` = 18

Area
= `sqrt(18(18 - 6)(18 - 14.4)(18 - 15.6)`
= `sqrt(18(12)(3.6)(2.4)`
= `sqrt(1866.24)`
= 43.2cm².