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Sagot :
Given:
Perimeter of rectangular wooden deck = 90 ft
Length is 5 feet less than 4 times its width.
Let's find the dimensions of the wooden deck.
Since the length is 5 feet less than 4 times its width, we have:
L = 4W - 5
Where:
L represents the length
W represents the width.
Now, apply the formula for the perimeter of a rectangle:
P = 2W + 2L
Where P is the perimeter.
Plug in 90 for P and (4W - 5) for L:
90 = 2W + 2(4W - 5)
Now, apply distributive property:
90 = 2W + 2(4W) + 2(-5)
90 = 2W + 8W - 10
90 = 10W - 10
10W = 90 + 10
10W = 100
Divide both sides by 10:
[tex]\begin{gathered} \frac{10W}{10}=\frac{100}{10} \\ \\ W=10 \end{gathered}[/tex]Substitute 10 for W in the first equation:
[tex]\begin{gathered} L=4(10)-5 \\ L=40-5 \\ L=35 \\ \end{gathered}[/tex]We have the solutions:
W = 10
L = 35
Therefore, the dimensions of the wooden deck are:
• Length of the wooden deck, L = 35 ft
,• Width of the wooden deck, W = 10 ft
ANSWER:
• Length of wooden deck = 35 ft
,• Width of wooden deck = 10 ft
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