Question

The sides of a triangle are in the ratio 15 : 13 : 14 and its perimeter is 168 cm. Find the area of the triangle.

Answer 1

Perimeter of the triangle = 168 cm

Sum of ratio of sides = 15 + 13 + 14 = 42

Let the first side =`(168xx15)/42` = 60 cm

Second side =`(168xx13)/42` = 52 cm

Third side =`(168xx14)/42` = 56 cm

Now, s =`"a + b + c"/2`

= `(60+52+56)/2=168/2=84`

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

= `sqrt(84(84-60)(84-52)(84-56))`

= `sqrt(84xx24xx32xx28)`

= `sqrt(2×2×3×7×2×2×2×3×2×2×2×2×2×2×2×7)`

= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7

= 1344 cm²