when the lenght of each side of a square is increased by 7in., its area is increased by 189in.^2. find the lenght of the side of the original square.
(s + 7)² = s² + 189
s² + 14 s + 49 = s² + 189
14 s = 140
To find the length of the side of the original square, let's break down the problem step by step.
Let's say the length of each side of the original square is "x" inches.
Thus, the area of the original square is x^2 square inches.
According to the problem, when the length of each side of the square is increased by 7 inches, the new length becomes (x + 7) inches.
So, the area of the new square is (x + 7)^2 square inches.
The problem tells us that the new square's area is increased by 189 square inches compared to the original square. Mathematically, we can express this as:
(x + 7)^2 - x^2 = 189
We can now solve this equation to find the value of "x."
Expanding and simplifying the equation:
(x^2 + 14x + 49) - x^2 = 189
14x + 49 = 189
Now, let's isolate the variable "x" by subtracting 49 from both sides:
14x = 189 - 49
14x = 140
To find the value of "x," divide both sides by 14:
x = 140/14
x = 10
Therefore, the length of each side of the original square is 10 inches.