Question

9. Suppose the perimeter of a triangle is given by

P = 13x + 5y, and two of its sides have lengths of
2x + y and 8x + 4y. What is the length of the third
side?

Answer 1

The length of the third side is 3x

Explanation:

Algebraic Expressions

This problem deals with the ability to manage algebraic expressions in two variables.

Recall the perimeter of a triangle is the sum of its three sides. We already know the perimeter of the triangle is:

P=13x+5y

We also know the lengths of two of its sides are 2x+y and 8x+4y. The sum of those sides is:

S2=2x+y+8x+4y

Joining like terms:

S2=10x+5y

The third side must be the difference between the perimeter and the sum above:

S3=13x+5y-(10x+5y)

Operating:

S3=13x+5y-10x-5y

Joining like terms:

S3=3x

The length of the third side is 3x