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What is the length of the room A rectangular room that is 2 feet longer than it is wide and the area of the room is 168 square feet?
The area of a rectangle: A = L x W
Let the length of W be x, so the length is L = x + 2. So,
A = LW
168 = (x + 2)x or
x (x + 2) = 168
x^2 + 2x + 168 add 1^2 to both sides to complete the square (1^2 = 1);
x^2 + 2x + 1 = 169 use formula (a + b)^2 = a^2 + 2ab + b^2
(x + 1)^2 = 169
x + 1 = ± √169 since the distance is positive, we can ignore the negative sign;
x + 1 = 13 subtract 1 to both sides;
x = -1 + 13
x = 12
x + 2 = 12 + 2 = 14
Thus the length of the room is 14 ft, and its wide is 12 ft.
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