Answer:
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
[tex]L+2W=58[/tex] ----> equation A
[tex]L=2W+6[/tex] ----> equation B
substitute equation B in equation A and solve for W
[tex]2W+6+2W=58[/tex]
[tex]4W+6=58[/tex]
[tex]4W=58-6[/tex]
[tex]4W=52[/tex]
[tex]W=13\ ft[/tex]
Find the value of L
[tex]L=2W+6[/tex] ----> [tex]L=2(13)+6=32\ ft[/tex]
therefore
The length of the patio is 32 ft and the width is 13 ft
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 = [tex]\frac{52}{4}[/tex]
= 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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