Question

The length of a rectangle is 4 ft. greater than the width. If each dimension is increased by 3,

the new area will be 45 square feet. Find the dimensions of the original rectangle.

Answer 1

Explanation:

Original rectangle:

Let width = x ft

Length = x + 4

New rectangle

length = x + 4 + 3 = x +7

Width = x + 3

Area = 45 sq. ft

length * width = 45

(x + 7)(x + 3) = 45

Use FOIL method

x*x + x*3 + 7*x + 7*3 = 45

x² + 3x + 7x + 21 = 45

x² + 10x + 21 - 45 = 0

x² + 10x - 24 = 0

x² + 12x - 2x - 12*2 = 0

x*(x + 12) - 2*(x + 12) = 0

(x + 12)(x - 2) = 0

x - 2 = 0

x = 2 {x +12 is ignored because measurement cannot have negative value}

Dimensions of the original rectangle:

Width = 2 ft

Length = 2 + 4 = 6 ft