Question

The base of an isosceles triangle is a third as long as the two equal sides (each, not

combined). Write the perimeter of the triangle as a function of the length of the base.

Answer 1

The perimeter is 7b

Explanation:

An isosceles triangle has exactly two sides of the same length. Suppose we have an isosceles triangle with the base as the unequal side length of b.

The perimeter of the triangle is:

P = x + x + b = 2x + b

Being x the two equal side lengths.

It's given the base b of the triangle is one-third of any of the other sides, that is:

b = 1/3 x

Or, equivalently:

x = 3b

Thus, the perimeter of the triangle is:

P = 2x + b = = 2(3b) + b

P = 6b + b = 7b

The perimeter is 7b