Question

the perimeter of any rectangle in which the length is 5 more than three times the width is ( p = 8w + 10 ), where ( w ) is the width. which formula can be used to find the width given the perimeter?

a) ( w = p - \frac{5}{4} )

b) ( w = \frac{p - 10}{8} )

c) ( w = -\frac{p + 10}{8} )

d) ( w = \frac{1}{8}p - 10 )

Explanation:

Step1: Start with the perimeter formula

We know the perimeter formula for the rectangle is \( P = 8w + 10 \). Our goal is to solve for \( w \) in terms of \( P \).

Step2: Subtract 10 from both sides

To isolate the term with \( w \), we subtract 10 from both sides of the equation. So, \( P - 10 = 8w + 10 - 10 \), which simplifies to \( P - 10 = 8w \).

Step3: Divide both sides by 8

Now, to solve for \( w \), we divide both sides of the equation \( P - 10 = 8w \) by 8. This gives us \( w=\frac{P - 10}{8} \).

Answer:

B. \( w=\frac{P - 10}{8} \)