The perimeter of a rectangle is 90 feet, and the length is 32 feet. What is the width of the rectangle? A. 26 feet
B. 13 feet
C. 58 feet
D. 15 feet

Length is 12ft, width is 4 ft.

2 x (length + width) = perimeter = 32 ft

⇒ length = 16ft - width [1]

length x width = area = 48 sq ft

Using [1] above:

⇒ (16ft - width) x width = 48 sq ft

multiplying out and rearranging:

⇒ width2 - 16 x width + 48 = 0

factorizing:

⇒ (width - 4)x(width - 12) = 0

Thus width = 4 or 12, so using [1] above:

⇒ width = 4ft, length = 16 - 4 = 12ft

or width = 12ft, length = 16 - 12 = 4ft

Convention is that the length is larger than the width, thus rectangle is 12ft long by 4 ft wide.

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