Problema Solution
A rectangle is 3 times as long as it wide. If the area is 108 square feet, find its perimeter._______ ft
A large rectangular movie screen in an Imax theater has an area of 10,764 square feet. Find the dimensions of the screen if it is 25 feet longer than it is wide.length___________ft width_____________ft
Answer provided by our tutors
If width is x feet, then length is 3x feet
So, area = length * width = (3x * x) square feet = (3x^2) square feet
Now, 3x^2 = 108
x^2 = 108/3
x^2 = 36
x = 6 (ignoring the negative root -6)
So, the perimeter = 2 * (length + width) = 2*(3x + x) feet = 2*4x feet = 8x feet = 8*6 feet = 48 feet
If width is w feet, then length is (w+25) ft.
So, the area = length * width = (w + 25)*w square feet
Now (w + 25)w = 10764
w^2 + 25w - 10764 = 0
w^2 + 117w - 92w - 92*117 = 0
(w + 117)(w - 92) = 0
w = -117, 92
As w cannot be negative, the only value of w = 92
So, length = w + 25 ft = 92 + 25 ft = 117 ft
and width = 92 ft