Question

A rectangle is 6 feet long and 4 feet wide. If each dimension is increased by the same number of feet, a new rectangle is formed whose area is 39 square feet more than the area of the original rectangle. By how many feet was each dimension increased?​

Answer 1

Each dimension increased by 3 ft.

Explanation:

Area of the original rectangle = 4 * 6 = 24 square feet

Increased dimension = x ft

New length = 6 + x

New width = 4 +x

New area = (6 + x)(4 +x) {Use FOIL method}

= 6*4 + 6*x + x*4 + x*x

= 24 + 6x + 4x + x²

= x² + 10x + 24

New area = 24 + 39

x² + 10x + 24 = 63

x² +10x + 24 - 63 = 0

x² + 10x - 39 = 0

x² + 13x - 3x - 3*13 = 0

x (x + 13) - 3(x + 13) = 0

(x + 13)(x -3) = 0 {Ignore x + 13, as it gives negative value}

x - 3 = 0

x = 3