When the length of each side of a square is increased by 5 inches, the AREA is increased by 85 in2. Find the length of the side of the original square
(x+5)^2 = x^2+85
...
To solve this problem, let's denote the length of each side of the original square as "x inches".
We are given that when the length of each side is increased by 5 inches, the area of the square is increased by 85 square inches.
The area of a square is given by the formula: Area = side^2.
So, the area of the original square is x^2 square inches.
When the length of each side is increased by 5 inches, the new side length becomes (x + 5) inches. The area of the new square is then (x + 5)^2 square inches.
According to the problem, the increase in area is 85 square inches.
Therefore, we can set up the equation:
(x + 5)^2 - x^2 = 85.
Expanding (x + 5)^2, the equation becomes:
x^2 + 10x + 25 - x^2 = 85.
Simplifying the equation, we have:
10x + 25 = 85.
Subtracting 25 from both sides, the equation becomes:
10x = 60.
Dividing both sides by 10, we find:
x = 6.
Therefore, the length of the side of the original square is 6 inches.