Question

The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third
side is 6 cm less than twice the smaller side. Find the area of the triangle.

Answer 1

Answer:

Let x be the smaller side. Then the second side becomes (x+4) and the third (2x-6).

Perimeter P=x+(x+4)+(2x-6)=50 cm

4x-2=50; x=13 cm

Side 1= 13 cm

Side 2=(13+4)cm=17 cm

Side 3=(26–6)cm=20 cm

s= (perimeter)/2=25 cm

Using Heron Formula, we get the triangle area A :

A^2=[ 25 (25–13)(25–17)(25–20)]=12,000 cm^4

A^2=12,000 cm^4

A=√12000 cm^2 (real Number) or Finally:

A= 109.54 cm^2