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
click here to see the step by step solution of the equation:
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.