The sides of a square are all increased by 3 cm. The area of the new square s 64 cm^2. How can you find the length of a side of the original square?
the ways above is probably easier, but my teacher probably wants me to solve it by factoring..
Since the formula for the a\area of a square is "Area=(side)^2", all the sides are equal. So just substitute in.
s^2=64
s=sqrootof64
side=8
8-3=5
so the original side length is 5 cm.
The area of a square is the two sides multiplied together.
Since all sides of a square are the same, you need to find the square root of 64.
When you find that, subtract 3 cm from it to answer your question.
To find the length of a side of the original square, you can follow these steps:
1. Let's assume the length of a side of the original square is x cm.
2. If the sides of the original square are increased by 3 cm, the length of a side in the new square would be (x + 3) cm.
3. The area of a square is calculated by multiplying the length of one side by itself. Therefore, the area of the new square is (x + 3) * (x + 3) cm^2, which is equal to 64 cm^2.
4. Simplifying the equation, we get (x + 3)^2 = 64.
5. Expanding the equation, we have x^2 + 6x + 9 = 64.
6. Rearranging the equation, we get x^2 + 6x - 55 = 0.
7. Now, we can solve this quadratic equation for x. It can either be factored or solved using the quadratic formula.
- By factoring: (x + 11)(x - 5) = 0. So, x can be either -11 or 5.
- By using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 1, b = 6, and c = -55. By substituting these values into the formula, you can calculate the two possible values for x.
8. However, since the length of a side cannot be negative, we can discard the solution x = -11.
9. Therefore, the length of a side of the original square is x = 5 cm.
By following these steps, you can find the length of a side of the original square, which is 5 cm.