Question

The isosceles triangle shown has a base of 4 y + 2 and a perimeter of 6 y + 12 .  Which expression represents the length of 1 of the triangle's legs?

Answer 1

The expression that represents the length of 1 of the triangle's legs is y + 5

Explanation:

An isosceles triangle has two sides equal which are the triangle legs. Let b represent the base of the triangle and l represent one of the triangle's legs. Then, the perimeter, P is given by

P = l + l + b

i.e P = 2l + b

From the question, P = 6y + 12 and b = 4y +2

∴ 6y + 12 = 2l + 4y + 2

6y - 4y + 12 - 2 = 2l

2y + 10 = 2l

∴ 2l = 2y + 10

Then,

l = (2y+10)/2

l = y + 5

Hence, the expression that represents the length of 1 of the triangle's legs is y + 5