Word problem involving areas of squares

The difference of the areas of two squares is 375 square feet. Each side of the larger square is four times the length of a side of the smaller square. Find the length of a side of each square.

x = side of small square
4x = side of large square   {each side of larger square is four times the length of a side of smaller square}

To get the area of a square, just square one side.

(4x)² - x² = 375   {difference of areas is 375}
16x² - x² = 375   {squared 4x}
15x² = 375   {combined like terms}
x² = 25   {divided both sides by 15}
x = 5   {took square root of both sides}
4x = 20   {substituted 5, in for x, into 4x}

each side of small square is 5 ft
each side of large square is 20ft

Ask Algebra House