Problema Solution

Find the dimensions of a rectangular Persian rug whose perimeter is 28 ft and whose area is 45 ft^2.

Answer provided by our tutors

let 'l' and 'w' represent the length and the width of the rectangular Persian rug, l>0, w>0, l>w


the perimeter of the rug is 28:


2(l + w) = 28 (since the perimeter of a rectangle is 2(length + width)


l + w = 28/2


l + w = 14


l = 14 - w


the area is 45 ft^2


l*w = 45 (since the are of a rectangle = length * width)


plug l = 14 - w into the last equation


(14 - w)*w = 45


by solving we find:


w1 = 9 ft


w2 = 5 ft


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for w = 9 ft we have l = 45/9 = 5 ft < 9 ft thus this not the solution.


for w = 5 ft we have l = 45/5 = 9 ft > 5 ft thus we found the solution l = 9 ft and w = 5 ft


the dimensions of the rectangular rug are: the length is 9 feet and the width is 5 feet.