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

the squares is 225 in. Find the lengths of the sides of the two squares.
A side of the small square is in.; a side of the big square is in.

Answer 1

small square side = 9 inches

large square side = 9 + 3 = 12 inches.

Explanation:

Let the smaller square have a side length of s

The the larger square have a side length of s + 3

Total area of the two squares is 225

Formula

s^2 + (s + 3)^2 = 225 Expand

Solution

s^2 + s^2 + 6s + 9 = 225

2s^2 + 6s + 9 = 225 Subtract 225 from both sides

2s^2 + 6s - 216 = 0 This factors.

( x - 9)(x + 12) = 0

x - 9 =0

x + 12 = 0

x = 9 is the only valid root for this question