A study area inside the living room has a width that is 4 inches less than the length. The area is 12 square inches. Find the dimensions. Use RESA (Represent, Equation, Solution, Answer)
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 :-) )