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
-2 + 34p 17p - 1
-9 + 16q + 34p -2q + 34p

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \).

Step2: Substitute the given length and width

Given width \( = (10p - 9q) \) and length \( = (7p + 8q) \), so we first find the sum of length and width: \( (10p - 9q)+(7p + 8q) \).
Simplify the sum: \( 10p - 9q + 7p + 8q = (10p + 7p)+(-9q + 8q)=17p - q \).

Step3: Multiply the sum by 2 to get the perimeter

Perimeter \( P = 2\times(17p - q) \).
Using the distributive property \( a(b + c)=ab + ac \), we have \( 2\times17p - 2\times q = 34p - 2q \).

Answer:

\( -2q + 34p \) (or the option corresponding to \( 34p - 2q \))