Question

the perimeter of a rectangular patio is 64 feet. the width of the patio is (x + 2) feet and the length of the patio is (x + 6) feet. use the sketchpad to draw a picture, label it, and use the perimeter to find the value of x. x = find the width of the patio. find the length of the patio.

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). We know \( P = 64 \) feet, length \( = (x + 6) \) feet, and width \( = (x + 2) \) feet. So we substitute these into the formula:
\[ 64 = 2\times((x + 6)+(x + 2)) \]

Step2: Simplify the equation

First, simplify the expression inside the parentheses: \( (x + 6)+(x + 2)=2x + 8 \). Then the equation becomes:
\[ 64 = 2\times(2x + 8) \]
Divide both sides by 2:
\[ 32 = 2x + 8 \]

Step3: Solve for \( x \)

Subtract 8 from both sides:
\[ 32 - 8 = 2x \]
\[ 24 = 2x \]
Divide both sides by 2:
\[ x = 12 \]

Step4: Find width of the patio

The width is \( (x + 2) \) feet. Substitute \( x = 12 \):
\[ \text{width} = 12 + 2 = 14 \text{ feet} \]

Step5: Find length of the patio

The length is \( (x + 6) \) feet. Substitute \( x = 12 \):
\[ \text{length} = 12 + 6 = 18 \text{ feet} \]

Answer:

s:

• For \( x \): \( x = 12 \)
• For width: The width of the patio is 14 feet.
• For length: The length of the patio is 18 feet.