Question

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's length would be 9 cm. If the length that we are looking for is x and the two equal side lengths are y; then our equation would be x+x+y. Which would be 2x+y = 23, 23 equals the perimeter of the triangle. The third side, which is 5 less than twice the length of one of the other sides, would change our equation to y=2x-5. So then 2x+y =23, and

2x-y=5, then

4y would equal 28,

which makes y= 7, so then x would equal 9.

Explanation:

x + x + (2x – 5) = 23

Answer 2

One of the two equal sides = S. Both of them = 2S. The third side is 2S-5. The perimeter is 2S+2S-5 and that's 23. So 4S-5= 23, then 4S=28, and S=7. The third side is 2S-5, and that's 9.