Please help with trying to solve the following; in particular how to get the correct equation set up.
The perimeter of a square is 64 cm and the area of the square is 192 cm. What is the length of width of the rectangle?
Thank you for your help.
clearly it is not a square.
192 has several factors:
4x48
6x32
8x24
12x16
...
so, which of those factor pairs adds up to half of 64?
Steve, thanks for responding, the question may have said rectangle. It was on a previous test and with a final coming up; I wanted to make sure I knew how to do. But I do have another one:
The question:
The perimeter of a rectangle is 34 inches and the area is 50 square inches. What is the length and the width of the rectangle.
Sorry about the previous question. Hope you can help. Thank you
Hmmm.
xy=50
2(x+y) = 34
The only factor pairs of 50 are
1,50
2,25
5,10
None of those add up to 17, so the sides will not be integers. To find them, you will need to solve a quadratic equation:
x+y=17
x + 50/x = 17
x^2-17x+50 = 0
Now just use the quadratic formula.
To solve this problem, let's start by setting up equations based on the given information.
Let's assume the length of one side of the square is "x" cm. Since a square has all sides equal, the perimeter of the square is given by 4 times the length of one side. So, the perimeter equation would be:
Perimeter of square = 4x
Given perimeter = 64 cm
Therefore, we can write the first equation as:
4x = 64
Next, we can find the area of the square by multiplying the length of one side twice. So, the area equation would be:
Area of square = x * x = x^2
Given area = 192 cm^2
Therefore, the second equation can be written as:
x^2 = 192
To find the length (or width) of the rectangle, we need to solve for x in these two equations.
Now, you can solve the equations simultaneously. One way to do this is by isolating a variable in one equation and substituting it into the other equation.
From the first equation, divide both sides by 4:
4x/4 = 64/4
Simplifying gives:
x = 16
Now, substitute the value of x into the second equation:
(16)^2 = 192
256 = 192
This is not true, which means there must be an error in the problem statement or a miscalculation. Please check the given information again or provide any additional details to help us solve it correctly.
If you have any further questions, feel free to ask!