Question

The side lengths of a triangle are given by the expressions 6x + 3, 7x + 4, and 3x – 2. Write and simplify a linear expression for the perimeter of the triangle.

Answer 1

Perimeter of a figure is the sum of all sides

$P=(6x+3)+(7x+4)+(3x-2)$

now remove parenthesis

$P=6x+3+7x+4+3x-2$

group

$P=(6x+7x+3x)+(3+4-2)$

and solve

$P=16x+5$

the linear expression is

$16x+5$

it is a linear expression because the greater exponent is 1