Question

the width of a rectangle measures $(10p - 9q)$ centimeters, and its length measures $(7p + 8q)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$\bigcirc -2 + 34p$
$\bigcirc 17p - 1$
$\bigcirc -9 + 16q + 34p$
$\bigcirc -2q + 34p$

Explanation:

Step1: Recall perimeter formula

Perimeter of rectangle: $P = 2(\text{length} + \text{width})$

Step2: Substitute given expressions

$P = 2[(7p + 8q) + (10p - 9q)]$

Step3: Combine like terms inside brackets

$P = 2[(7p + 10p) + (8q - 9q)] = 2(17p - q)$

Step4: Distribute the 2

$P = 2\times17p + 2\times(-q) = 34p - 2q$

Answer:

$\boldsymbol{-2q + 34p}$ (matches the fourth option)