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

Answer:

$18\; {\rm in}$.

Step-by-step 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 $18\; {\rm in}$.