Question

The length of a rectangle is (X + 8) and the width is (x - 3). Find the dimensions of the rectangle if the area is 42 square inches.

Answer 1

Length = 14 inches

Width = 3 inches

Explanation:

length * width = area

(x + 8 ) (x - 3) = 42

Use FOIL method

x*x - x*3 + 8*x - 8*3 = 42

x² -3x + 8x - 24 = 42

x² + 5x - 24 - 42 = 0

x² + 5x - 66 = 0

Sum = 5

Product = 66

Factors = 11 , (-6)

x² + 5x -66 = 0

x² + 11x - 6x - 6*11 =0

x(x + 11) - 6(x + 11) = 0

(x + 11) (x -6) = 0

x + 11 is ignored because length and width will not have negative value.

x - 6 = 0

x = 6

Length = x + 8 = 6 + 8 = 14 inches

Width = x - 3 = 6 - 3 = 3 inches