A square flower bed is to be enlarged by adding 2 meters in each side. If the larger square has an area of 196 square meters, what is the length of the original square?
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To solve this problem, we need to determine the length of the original square flower bed before it was enlarged. Let's break it down step by step.
1. Let's suppose the length of the original square flower bed is 'x' meters.
2. According to the problem, the larger square, after the enlargement, has an area of 196 square meters. This means the length of the larger square is 'x + 2' meters.
3. The formula for calculating the area of a square is length * width, or simply length^2.
4. So, the area of the larger square is (x + 2)^2 = 196.
5. Expanding the equation, we have x^2 + 4x + 4 = 196.
6. Rearranging the equation, we get x^2 + 4x - 192 = 0.
7. Now, we can solve this quadratic equation either by factoring or by using the quadratic formula.
8. Factoring: We need to find two numbers that multiply to -192 (product of the coefficients of x^2 and the constant term) and add up to 4 (coefficient of x). After trying different pairs, we find that the numbers are 12 and -16.
So, (x + 12)(x - 16) = 0.
This gives us two possible solutions: x + 12 = 0 or x - 16 = 0.
Solving these equations, we find x = -12 or x = 16.
Since the length cannot be negative, we discard x = -12.
9. Therefore, the length of the original square flower bed is x = 16 meters.
So, the length of the original square flower bed is 16 meters.