Each of the two congruent sides of an isosceles traingle is

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

Solution

Lets call the base x
Base=x
Given: Each of the two congruent sides of an isosceles triangle is 8 inches less than twice the base.
Express this in terms of x
2x-8
Given: perimeter of the triangle is 74 inches
Now use formula for perimeter of triangle to solve for x
(firstside)+(secondside)+(base)=perimeter
(2x-8)+(2x-8)+(x)=74
2x-8+2x-8+x=74 combine like terms
5x-16=74 add 16 to both sides
5x=90 divide both sides by 5
x=18
Answer: The base is 18 inches
Both of the remaining sides equal 2x-8
so replace x with 18 to find length of each side
2(18)-8
36-8
28
Congruent sides are 28 inches each.
Check answers:
sum of all sides should equal 74
28+28+18=74
74=74