Question

Modeling and Solving a Problem:
An isosceles triangle has two sides of equal length. The third side is 5 less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm, what is the length of the third side?

Explain how you would define a variable for this problem.

Answer 1

The third side is 9 cm long

Let $x$ represent one of the equal sides. Then the` other side will be $2x-5$.

Adding all the length of the sides should give 23. Thus,

$x+x+2x-5=23$

This implies that,

$4x-5=23$

We group like terms and simplify to obtain.

$4x=23+5$

$4x=28$

Divide through by 4 to get

$x=7$

Hence the length of the other side is

$2(7)-5=9$