Representation:
x = length
x- 4 = width ( four inches less than the length)
12 square inches = Area
Use the formula Area = L × W to find the dimensions.
Equation:
L × W = Area
(x) (x-4) = 12
Solution:
x² - 4x = 12
Transform to quadratic equation, ax² + bx + c = 0
x² - 4x - 12 = 0
Solve by factoring:
(x - 6) (x + 2) = 0
x - 6 = 0 x + 2 = 0
x = 6 x = -2
Choose the positive root, x = 6
Answer:
Length = x ⇒ x = 6 inches
Width = x - 4 ⇒ 6 - 4 = 2 inches
The dimensions are 6 inches for length and 2 inches for width.
To check:
(6 inches) (2 inches) = 12 square inches
12 square inches = 12 square inches.
(On a lighter note: Who wants to be in a study area with dimensions of 2 inches and 6 inches? An adult shoe size is at average 7 to 8 inches. Not even a left or right shoe would fit in. This problem is not a real-life application. Or maybe, it's just me :-) )