Question

The side lengths of a triangle are given by the expressions 5x+3, 5x+5, and 3x–2. Write and simplify a linear expression for the perimeter of the triangle.

A. 13x–4
B. 13x+6
C. 10x+6
D. 10x–4

Answer 1

The perimeter of the triangle with sides 5x+3, 5x+5, and 3x-2 is calculated by adding the expressions yielding the linear expression 13x+6, which corresponds to option B.

Step-by-step explanation:

To find the perimeter of a triangle with side lengths given by expressions, we simply add those expressions together. For the triangle with sides of lengths 5x + 3, 5x + 5, and 3x - 2, the perimeter P can be calculated as follows:

• P = (5x + 3) + (5x + 5) + (3x - 2)
• P = 5x + 5x + 3x + 3 + 5 - 2
• P = 13x + 6

Therefore, the perimeter expressed as a linear expression and simplified is 13x + 6, which corresponds to option B.