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.
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What don't you understand about it?
Let's assume the length of each side of the original square is "x" inches.
According to the problem, when the length of each side is increased by 7 inches, the new length becomes "x + 7" inches.
The area of a square is calculated by multiplying the length of one side by itself, so the area of the original square is x^2 square inches.
Similarly, the area of the new square is (x + 7)^2 square inches.
It is given that the area of the new square is increased by 189 square inches compared to the original square. So, we can write the equation:
(x + 7)^2 = x^2 + 189
Expanding the equation:
x^2 + 14x + 49 = x^2 + 189
Subtracting x^2 from both sides of the equation:
14x + 49 = 189
Subtracting 49 from both sides of the equation:
14x = 140
Dividing both sides of the equation by 14:
x = 10
Therefore, the length of each side of the original square is 10 inches.
To find the length of the side of the original square, we can start by considering the given information. Let's denote the original length of each side of the square as "x".
According to the problem, when the length of each side is increased by 7 inches, the new length becomes "x + 7". Additionally, we know that the new area of the square (with the increased sides) is 189 in^2 greater than the original area.
The area of a square is calculated by squaring the length of one of its sides. So, the original area is x^2, and the new area is (x + 7)^2.
From the given information, we also know that the new area is 189 in^2 greater than the original area. Mathematically, this can be written as:
(x + 7)^2 - x^2 = 189
To solve this equation and find the value of x, we can follow these steps:
1. Expand the equation:
x^2 + 14x + 49 - x^2 = 189
2. Simplify the equation by canceling out the x^2 terms:
14x + 49 = 189
3. Subtract 49 from both sides of the equation:
14x = 140
4. Divide both sides of the equation by 14:
x = 10
Therefore, the length of the side of the original square is 10 inches.