Question

one side of an isosceles triangle is three times as long as another side of the triangle. If the perimeterof the triangle is 140, then what is the length of the base of the triangle?

Answer 1

20

Explanation:

P, perimeter of triangle = a + b + c

We're given P = 140 and it is an isosceles triangle.

We can change P to be 2a + b since 2 sides are equal in an isosceles

So, 140 = 2a + b

One side is 3x longer than the other. The equal sides in the triangle can not be 3x longer than each other since it is equal.

And the isosceles sides are longer than the 1 base side.

So if a = our isosceles sides, and b is our base side, than a is 3x our base side which can be written as a = 3b

Now, 140 = 2(3b) + b, and we can now solve

140 = 6b + b => 140 = 7b

20 = b

Our base length is 20.