Question

1. find the dimensions of a rectangle that has a perimeter of 184 inches in which the length is 4 less than 5 times greater than the width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( 5w - 4 \) inches (since length is 4 less than 5 times the width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 184 \), so substitute \( l = 5w - 4 \) into the formula:
\[
184 = 2((5w - 4) + w)
\]

Step3: Simplify the equation

First, simplify inside the parentheses:
\[
184 = 2(6w - 4)
\]
Then distribute the 2:
\[
184 = 12w - 8
\]

Step4: Solve for \( w \)

Add 8 to both sides:
\[
184 + 8 = 12w
\]
\[
192 = 12w
\]
Divide both sides by 12:
\[
w = \frac{192}{12} = 16
\]

Step5: Find the length

Substitute \( w = 16 \) into \( l = 5w - 4 \):
\[
l = 5(16) - 4 = 80 - 4 = 76
\]

Answer:

The width of the rectangle is 16 inches and the length is 76 inches.