Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 6 feet longer than twice its width. find the length and width of the patio.

The required patio length(L) = 32 and width(w) = 13.

Given that,

Wayne is hanging a string of lights 58 feet long,

And the side along the house, is 6 feet long.

We have to find,

The length and width of the patio.

According to the question,

Let, the length of his patio be L and width w,

Wayne is hanging a string of lights 58 feet long around the three sides of his patio, which is adjacent to his house.

L + 2W = 58

And The length of his patio, the side along the house, is 6 feet longer than twice its width.

L = 2W + 6

Solving the equation putting the of L from equation 2 in equation 1,

= 2W + 6 + 2W = 58

= 4W = 58 - 6

= 4W = 52

= W =

= W = 13

And L = 2(13) + 6 = 32

Patio length(L) = 32 And width(w) = 13.

Hence , The required patio length(L) = 32 And width(w) = 13.

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The length of the patio is 32 ft and the width is 13 ft

Step-by-step explanation:

see the attached figure to better understand the problem

Let

L ----> the length of his patio

W ---> the width of his patio

we know that

----> equation A

----> equation B

substitute equation B in equation A and solve for W

Find the value of L

 ---->

therefore

The length of the patio is 32 ft and the width is 13 ft

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.