Respuesta :
The lengths of the sides of the triangle are 8, 8, 20
Explanation:
Given that the perimeter of an isosceles triangle is 36 inches.
The base of the triangle is [tex]2\frac{1}{2}[/tex] times longer than each of its legs.
We need to determine the lengths of the sides of the triangle.
Lengths of the sides:
Let x denote the lengths of the sides of the triangle.
The base of the triangle is given by
[tex]2\frac{1}{2}x=\frac{5}{2}x=2.5x[/tex]
Perimeter of the isosceles triangle = Sum of the three sides of the triangle.
Thus, we have,
[tex]36=x+x+2.5x[/tex]
[tex]36=4.5x[/tex]
[tex]8=x[/tex]
Thus, the length of the sides of the isosceles triangle is 8 inches.
Base of the triangle = [tex]2.5(8)=20 \ inches[/tex]
Hence, the three sides of the isosceles triangle are 8, 8, 20
