4. The length of a rectangle exceeds its width by 6 units. If each dimension were increased by 3 units, the area would be increased by 57 square units. Find t

Question

4. The length of a rectangle exceeds its width by 6 units. If each dimension were increased by 3 units, the area would be increased by 57 square units. Find the dimensions of the rectangle.

Answer 1

Hi Samuel;

 

Original rectangle:

L = w + 6

Area = Lw = (w+6)(w) = w² + 6w

 

New rectangle:

L+3 = w+6+3 = w + 9 for length

w+3 = width

Area = Lw = (w+9)(w+3) = w² + 12w + 27

 

Since the 2nd area is 57 units more than the first area:

 

w² + 6w + 57 = w² + 12w + 27

 

-6w = -30

w = 5 units

 

L = w+6 = 11 units

 

The original rectangle is 11 by 5 units with area of 55 units²

New rectangle is 14 by 8 units with area of 112 units²