Algebra worded problem

Question

The combined area of a square and a rectangle is 57 square feet. The width of the rectangle is 3 feet more than the length of a side of the square, and the length of the rectangle is 5 feet more than the length of a side of the square. Fimd the length of the rectangle.

Answer 1

Square: A = s²

 

Rectangle: A = (s + 3)(s + 5) = s² + 8s + 15

 

2s² + 8s + 15 = 57

2s² + 8s - 42 = 0

s² + 4s - 21 = 0

(s + 7)(s - 3) = 0

 

s + 7 = 0

s = -7

Doesn't apply because we don't measure in negative numbers.

 

s - 3 = 0

s = 3

 

3 + 5 = 8