Quadratic Word Problem

Question

Steps to take:

1. Draw diagrams
2. Decide what X will stand for
3. Write an equation that uses the variable and the info they give you
4. Set the equation equal to zero
5. Factor
6. Solve

 

Word Problem: There are two squares. The larger square has a side length one foot greater than that of the smaller square. If the combined area of two squares is 113 square feet, find the length of the side of the smaller square.

Answer 1

113 = s^2 + (s+1)^2 = s^2 + s^2 + 2s +1

2s^2 +2s - 112 =0

s^2 + s - 56 = 0

(s-7)(s+8) = 0

s = 7 feet = side of smaller square

8 feet = side of the larger square

8^2 + 7^2 = 64+49 = 113