Question

A rectangle patio has a perimeter of 38 feet. If the length of the patio is 5 feet less than twice the width, find the dimensions of the patio

Answer 1

The length is 11ft.

The width is 8ft.

Explanation:

Hello!

Perimeter of a rectangle:
`P = 2(l + w)`

• P = perimeter
• l = length
• w = width

We know that the length is 5 ft less than twice the width, which can be expressed by the equation: l = 2w - 5. We can plug in 38 for "P".

We can substitute the equation for l, and solve for the width.

Solve for W

• 
  `P = 2(l + w)`
• 
  `38 = 2((2w - 5) + w)`
• 
  `38 = 2(3w - 5)`
• 
  `38 = 6w - 10`
• 
  `48 = 6w`
• 
  `8 = w`

The width is 8. We can solve for the length by plugging it back into the equation l = 2w - 5

Solve for L

• l = 2w - 5
• l = 2(8) - 5
• l = 16 - 5
• l = 11

The length is 11.

The dimensions are 11 ft and 8 ft.