Formula for perimeter of a rectangle = 2(L + W)
let the number be x
width = 2x + 8
length = 3(2x + 8)
substitute respectively
96 = 2 (2x + 8 + 3(2x + 8)) open the bracket
96 = 2 ( 2x + 8 + 6x + 24) collect like terms
96 = 2 (8x + 32) open the bracket
96 = 16x + 64
collect like terms
96 - 64 = 16x
32 = 16x
divide both sides by 16
32/16 = 16x/16
2 = x
therefore, the width = 2x + 8 = 2(2) + 8 = 4 + 8 = 12.
and the length = 3(2x + 8) = 6x + 24 = 6(2) + 24 = 12 + 24 = 36.
The length and width of the fence should be made 76.25 feet and 23.75 feet respectively. Also, the expression for the length is L = 3W + 5 and the perimeter is P = 2(4W + 5).
<h3>How to determine the fence's dimension?</h3>
Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
<u>Where:</u>
- P is the perimeter of a rectangle.
- L is the length of a rectangle.
- W is the width of a rectangle.
Since the length of this fence is 5 more than 3 times the width, we have:
L = 3W + 5
Substituting the given parameters into the formula, we have;
200 = 2(3W + 5 + W)
200 = 2(4W + 5)
200 = 8W + 10
8W = 190
W = 190/8
W = 23.75 feet.
For the length, we have:
L = 3W + 5
L = 3(23.75) + 5
L = 76.25 feet.
Read more on perimeter of a rectangle here: brainly.com/question/17107023
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Answer:
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Step-by-step explanation:
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