We conclude that the length of the rectangle is 17 ft, and the width of the rectangle is 95ft.
How to find the length and width of our rectangle?
Remember that for a rectangle of width W and length L, the perimeter is:
P = 2*(L + W)
Here we know that the perimeter is 224 ft, and we know that the length length is an odd integer, then:
L = (2n + 1)
The width is 5 times the next odd integer, then:
W = 5*(2n + 3)
Where n is an integer number. Replacing all that in the perimeter equation, we get:
224 = 2*( (2n + 1) + 5*(2n + 3))
Now we just need to solve this for n.
224/2 = ( (2n + 1) + 5*(2n + 3))
112 = (2n + 1) + 5*(2n + 3) = 2n + 1 + 10n + 15 = 12n + 16
112 - 16 = 12n
96 = 12n
96/12 = n = 8
Then the length is:
L = (2n + 1) = (2*8 + 1) = 17
And width:
W = 5*(2n + 3) = 5*(19) = 95
We conclude that the length of the rectangle is 17 ft, and the width of the rectangle is 95ft.
If you want to learn more about rectangles:
https://brainly.com/question/17297081
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