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Answer :
Hello from MrBillDoesMath!
Answer:
L = 35, W = 25
Discussion:
The attachment shows that
P = 2L + 2W = 120
and
L = 10 + W
2L + 2W = 120 => Substitute the last equation into the first one
2(10 + W) + 2W = 120 =>
20 + 2W + 2W = 120 => combine like terms
20 + 4W = 120 => subtract 20 from both sides
4W = 120 -20 = 100 => divide both sides by 4
W = 100/4 = 25
Hence, L = 10 + W = 10 + 25 = 35
Thank you,
MrB
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Final answer:
To find the dimensions of the rectangle with a perimeter of 120 feet and a length that is ten feet more than the width, we set up an equation based on the perimeter formula. Solving this, we find the width to be 25 feet and the length to be 35 feet.
Explanation:
To determine the dimensions of the rectangle, we need to set up an equation based on the perimeter and the given relationship between the length and width. The formula for the perimeter (P) of a rectangle is P = 2(length) + 2(width). Since it's given that the perimeter is 120 feet, and the length is ten feet more than the width, we can express this as:
P = 2(width + 10) + 2(width)
Now, let's find the width (w) and the length (l).
Let the width be w, then the length would be w + 10 feet (since it is ten feet more than the width).
Substitute this into the perimeter formula: 120 = 2(w + 10) + 2w.
Simplify the equation: 120 = 2w + 20 + 2w -> 120 = 4w + 20.
Subtract 20 from both sides: 100 = 4w.
Divide both sides by 4 to find the width: w = 25 feet.
Therefore, the length is l = w + 10 = 35 feet.
So, the width of the rectangle is 25 feet and the length is 35 feet.
