Question

Each of the two congruent sides of an isosceles triangle is 8 inches less than twice the base. The perimeter is 74 inches. What is the length of the base?

Answer 1

`18\; {\rm in}`.

Explanation:

Let
`(x\; {\rm in})` be the length of the base.

The question states that the length of each congruent side is
`8\; {\rm in}` less than twice the length of the base. Twice the length of the base would
`(2\, x\; {\rm in})`. The length of each congruent side would be
`(2\, x - 8)\; {\rm in}`.

Sum up the length of each side to find the perimeter of this triangle:

`(2\, x - 8) + (2\, x - 8) + x = 5\, x - 16`.

Substitute in the actual perimeter of this triangle:

`5\, x - 16 = 74`.

Solve for
`x`:

`x = 18`.

Therefore, the length of the base of this isosceles triangle would be
`18\; {\rm in}`.