The area of a rectangle is 270 square feet. The ratio of the width to the length is 5:6. How do you find the length and the width?

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Answer 1 · 2016-02-14T00:28:22

Solve to find length #18# ft and width #15# ft.

Since we are told that the ratio of the width to the length is #5:6# then let the width be #5t# ft and length be #6t# ft for some #t#.

The area is #270 = (5t)(6t) = 30t^2#

Divide both ends by #30# to find:

#t^2 = 9#

Hence #t=+-3#

Since we're dealing with a real rectangle, we require #t > 0# so that the width and length are positive, so #t=3#

The width is then #5t = 15# ft and length #6t = 18# ft.