Math word problem help. Thanks!

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 areas of the squares is 485 in2. Find the lengths of the sides of the two squares.

 

a side of the small square is ____ a side of the big square is ____?

Answer 1

x = side of small square

 

x² + (x +3)² =285

x² + (x+3)(x+3) = 285

x² + x² + 3x + 3x + 9 = 285  (using FOIL)

2 x ² + 6 x + 9 = 285

                 - 9     - 9

2x² + 6 x = 276

2 ( x² + 3x) = 276

             divide by 2

x² + 3x = 188

x² + 3x - 188 = 0

(x - 14) (x + 17)

side of small square is 14, side of large square is 17

 

Answer 2

Here's what we know:

x = y + 3 (the length of one square side is larger by 3)

x² + y² = 485 (the areas of the squares equals 485 in²)

 

Plug in the value:

(y + 3)² + y² = 485

Distribute:

y² + 6y + 9 + y² = 485

Combine like:

2y² + 6y + 9 = 485

Subtract 485:

2y² + 6y - 476 = 0

Divide by 2:

y² + 3y - 238 = 0

Due to the middle monomial being small, we know the two factors have to be close together)

(y + 17)(y - 14) = 0

y = -17, 14

We can't have a negative length, so y = 14

 

x = 14 + 3

x = 17

 

14² + 17² = 485

196 + 289 = 485

485 = 485