College Algebra word problems

Question

The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the area of the squares is 317in². Find the lengths of the sides of the two squares.

Answer 1

Hi Emily,

 

We have two squares.

 

The smaller square has a side measure, x

The larger square has a side measure, x+3

 

The area of the smaller square is x²

The area of the larger square is (x+3)²

 

The sum of the areas of the two squares is x² + (x+3)² = 317

 

Clean up the equation so that you can solve for x

 

x² + x² + 6x + 9 = 317

2x² + 6x - 308 = 0

x² + 3x - 154 = 0

(x+ 14)(x-11) = 0

x +14 = 0       x-11=0

x = -14           x=11

 

We can throw out the solution x=-14 since a length cannot be a negative number, so x =11

 

The length of a side of the smaller square is 11".

The length of a side of the larger square is 14".

Answer 2

Let's start with defining the variables. 

 

Let S = length of one side of the smaller square (in inches)

 

Let L = length of one side of the larger square (in inches)

 

To help us finish the problem, we know three things.

1. The area, A, of a square with side length x is: A = x².

2. The side length of the larger square is 3 inches more than the side length of the smaller square: L = S + 3.

3. The combined area of both squares is 317 square inches: L² + S² = 317.

 

At this point, solve the equation in terms of one of the variables. Then you can determine the areas of both squares.