Question

The perimeter of a rectangle is 224 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.

1. 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.