Can someone get me in the right direction to figure this problem?
The sides of a square are lengthened by 7 cm. The area becomes 256 cm^2 Find the length of one of the sides of the original square.
Much appreciated
Area of square = height * length. Since they are equal in a square, Area = Side Squared (A = s^2)
To get the new area, you need (s + 7)^2 = 256. Solve for s. Hint: What is the square root of 256?
I hope this helps. Thanks for asking.
The vertex and line of symmetry is constantly confusing me and I know how to do it can you help me get started to find all of the different needs of this question
f(x)=2x^2 +2x +8I need the x coordinates of the vertex, the y coordinates of the vertex the equation of the line of symmetry and the max/min of f(1/2) =17/2 is a min or max
I have been working on this and may have confused myself. I appreciate any help.
Certainly! I'd be happy to help you figure out this problem.
To start, let's denote the length of one side of the original square as "x" cm.
According to the problem, when the sides of the square are lengthened by 7 cm, the new square has an area of 256 cm^2.
To find the length of one of the sides of the original square, we can set up the following equation:
(x + 7)^2 = 256
Here's how you can solve it step-by-step:
1. Expand the left side of the equation:
x^2 + 14x + 49 = 256
2. Move all terms to one side to set the equation equal to zero:
x^2 + 14x + 49 - 256 = 0
3. Simplify the expression on the left side:
x^2 + 14x - 207 = 0
4. Now, you can solve this quadratic equation for x. There are a few ways to do this, but one common method is factoring. However, in this case, factoring may not be viable. So, let's use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values are:
a = 1, b = 14, c = -207
Plugging in these values, we have:
x = (-14 ± √(14^2 - 4 * 1 * -207)) / (2 * 1)
Simplifying further:
x = (-14 ± √(196 + 828)) / 2
x = (-14 ± √1024) / 2
x = (-14 ± 32) / 2
5. Perform the calculations:
x = (-14 + 32) / 2 or x = (-14 - 32) / 2
x = 18 / 2 or x = -46 / 2
x = 9 or x = -23
Since we are dealing with the length of a side, the negative value (-23) doesn't make sense in this context. Therefore, the length of one of the sides of the original square is 9 cm.
I hope this explanation helps! Let me know if you have any further questions.