Homework Word Problem

Question

(1 point) Each side of a square is lengthened by 3 inches. The area of the new, larger square is 81 square inches. Find the length of a side of the original square.
Note: The formula for the area of a square is Area=side^2

a) Write the polynomial equation for the area of the larger square. Use the variable s to represent the length of the side of the original square.
Answer: 

b) Solve the equation and give the length of the side of the original square. Use inches for units.
Length: 

Answer 1

If the original square has side length s, then the new, larger square has side length (s + 3)

 

(s + 3)² = 81

s² + 6s + 9 = 81

s² + 6s - 72 = 0

(s - 6)(s + 12) = 0

s = 6 and s = -12

 

Since side lengths cannot be negative, the only plausible answer is s = 6 in.