Question

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?

Answer 1

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`