Question

if the length of the sides of a triangle are proportion 4:2:3 and the perimeter of the triangle 36cm theb the area of the triangle?

Answer 1

let the site before 4x, 2x and 3x.
perimeter = 36 cm
4x + 2x + 3x = 36
9x = 36
x = 36/9
x = 4

first side = 4x = 4 × 4 = 16 cm
second side = 2x = 2 × 4 = 8 cm
third side = 3x = 3 × 4 = 12 cm

Area = √[s(s-a)(s-b)(s-c)]
where s = a+b+c/2
a is equal to 16cm
b is equal to 8 cm
c is equal to 12 cm
16+8+12/2=s
36/2=s
s=18

s-a = 18 - 16 = 2
s-b = 18 - 8 = 10
s-c = 18 - 12 = 6

√18 × 2 × 10 × 6
√2×2×2×2×3×5×3×3
2×2×3√5×3
12√15sq.cm

Area of the triangle = 12√15sq.cm




Hope it helps you .