Question

question
the width of a rectangle measures (4s + 5) centimeters, and its length measures (2s - 10) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?

answer
-5 + 6s
12s - 10
-16 + 18s
9s - 8

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 \( = (4s + 5) \) cm and length \( = (2s - 10) \) cm. Substitute these into the formula:
\( P = 2\times[(4s + 5)+(2s - 10)] \)

Step3: Simplify the expression inside the brackets

First, combine like terms inside the brackets: \( (4s + 2s)+(5 - 10)=6s - 5 \)

Step4: Multiply by 2

Now, multiply the result by 2: \( P = 2\times(6s - 5) \)
Using the distributive property \( a(b + c)=ab + ac \), we get \( 2\times6s - 2\times5 = 12s - 10 \)? Wait, no, wait, let's check again. Wait, \( (4s + 5)+(2s - 10)=4s + 2s+5 - 10 = 6s - 5 \). Then \( 2\times(6s - 5)=12s - 10 \)? But wait, that's one of the options, but let's check the options again. Wait, maybe I made a mistake. Wait, no, wait the options: one of them is \( 12s - 10 \), but let's check the calculation again. Wait, width is \( 4s + 5 \), length is \( 2s - 10 \). Perimeter is \( 2\times(\text{width}+\text{length}) = 2\times(4s + 5 + 2s - 10)=2\times(6s - 5)=12s - 10 \). But wait, the options include \( 12s - 10 \) as one of the choices. Wait, but let's check the other options. Wait, maybe I miscalculated. Wait, no, let's do it again:

Width: \( 4s + 5 \)

Length: \( 2s - 10 \)

Perimeter \( P = 2\times(\text{length} + \text{width}) = 2\times[(4s + 5)+(2s - 10)] \)

Simplify inside the brackets: \( 4s + 2s + 5 - 10 = 6s - 5 \)

Multiply by 2: \( 2\times(6s - 5) = 12s - 10 \)

So the expression for the perimeter is \( 12s - 10 \).

Wait, but let's check the options: the options are:

• \( -5 + 6s \)

• \( 12s - 10 \)

• \( -16 + 18s \)

• \( 9s - 8 \)

So the correct answer should be \( 12s - 10 \).

Wait, but let's confirm. Wait, maybe I made a mistake in the sign. Wait, \( 5 - 10 = -5 \), so inside the brackets is \( 6s - 5 \), then \( 2\times(6s - 5)=12s - 10 \). Yes, that's correct. So the answer is \( 12s - 10 \).

Wait, but let's check the options again. The option \( 12s - 10 \) is present. So that's the correct one.

Answer:

\( 12s - 10 \) (the option with text "12s - 10")