The 3 side lengths of a right- angled triangle are 3x cm, 4x cm and 5x cm. If the perimeter of the triangle is 36 cm, what is the area of the triangle?

Question

asked Mar 13, 2023 62.1k views

1 Answer

Levi Fuller · Answer 1 · 2023-03-19T20:12:27+0000

Answer: the area of the triangle = 10.5 cm²

Explanation:

Let 3x=a, 4x=b, 5x=c.

Hence,

P=2*(a+b+c)

36=2*(3x+4x+5x)

36=2*12x

36=24x

Divide both parts of the equation by 24:

1.5 cm=x

a=3x

a=3*1.5

a=4.5 cm

b=4x

b=4*1.5

b=6 cm

c=5x

c=5*1.5

c=7.5 cm

$\displaystyle\\S=(a*b)/(2) \\\\S=(4.5*6)/(2) \\\\S=3.5*3\\\\S=10.5\ cm^2$