If the sides of a square lengthened by 7cm,the area becomes 196cmsquare. What is the length of the orinal side of the original square?
The first thing that you need to do is figure out the length of the sides when the area is 196. To do this you find the square root which is 14 cm. That means that each side is currently 14cm. Since they were lengthened by 7 cm, you subtract 7 cm from 14 cm to get the original length of the side which is 14-7= 7cm
Thanks. I made it harder than it was.
To solve this problem, we can follow these steps:
1. Let's assume the length of the original side of the square is "x" cm.
2. According to the given information, if all sides of the square are lengthened by 7 cm, the new side length becomes "x + 7" cm.
3. The new area of the square is given as 196 square cm.
4. The formula to calculate the area of a square is side length multiplied by side length, or A = side * side.
5. Using the above formula, we can write the equation: (x + 7) * (x + 7) = 196.
6. Expanding the equation gives us: x^2 + 14x + 49 = 196.
7. Rearranging the equation by subtracting 196 from both sides: x^2 + 14x + 49 - 196 = 0.
8. Simplifying further, we get: x^2 + 14x - 147 = 0.
9. Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula.
10. Factoring the equation gives us: (x - 7)(x + 21) = 0.
11. From this, we find two possible solutions: x - 7 = 0 or x + 21 = 0.
12. Solving these equations separately, we find: x = 7 or x = -21.
13. Since side lengths cannot be negative, we disregard x = -21.
14. Therefore, the length of the original side of the square is 7 cm.