Question
The sides of a square is 4y-3, 5y-3x, y+3x, 4x+1. Find x and y and the area of the square
Answers
Bot
Since all sides of a square are equal, we can set any two sides equal to each other and solve for x and y.
Setting (4y-3) = (5y-3x), we can simplify and get x = (5y-4y+3)/3 = y/3.
Setting (4y-3) = (y+3x), we can simplify and get x = (4y-3-y)/3 = y/3-1.
Setting (4y-3) = (4x+1), we can simplify and get x = (4y-4)/4 = y-1.
So we have three equations for x and y:
x = y/3
x = y/3-1
x = y-1
We can set any two of these equal to each other and solve for x and y.
Setting y/3 = y/3-1, we can simplify and get y = 3. Then we can plug this value of y into any of the three equations for x and get x = 1.
So the sides of the square are 9, 12, 6, and 5. The area of the square is (9)^2 = 81.
Setting (4y-3) = (5y-3x), we can simplify and get x = (5y-4y+3)/3 = y/3.
Setting (4y-3) = (y+3x), we can simplify and get x = (4y-3-y)/3 = y/3-1.
Setting (4y-3) = (4x+1), we can simplify and get x = (4y-4)/4 = y-1.
So we have three equations for x and y:
x = y/3
x = y/3-1
x = y-1
We can set any two of these equal to each other and solve for x and y.
Setting y/3 = y/3-1, we can simplify and get y = 3. Then we can plug this value of y into any of the three equations for x and get x = 1.
So the sides of the square are 9, 12, 6, and 5. The area of the square is (9)^2 = 81.
Surayya
I don’t still understand please explain
Bot
Sure, no problem. We are given the four sides of a square, which are as follows:
- 4y - 3
- 5y - 3x
- y + 3x
- 4x + 1
We know that all four sides of a square are equal in length. So we take any two sides and set them equal to each other, and then we can solve for the values of x and y that make them equal.
For example, let's take the first two sides and set them equal:
4y - 3 = 5y - 3x
We can simplify this equation by subtracting 4y from both sides:
-3 = y - 3x
Then we can add 3x to both sides:
3x - y = -3
This is one equation that relates x and y, based on the first two sides of the square. We can do the same thing with any two sides to get another equation.
If we set the first and third sides equal:
4y - 3 = y + 3x
We can simplify this equation by subtracting y from both sides:
3y - 3 = 3x
Then we can divide both sides by 3:
x = y - 1
This is another equation that relates x and y, based on the first and third sides of the square. If we set the first and fourth sides equal, we get another equation:
4y - 3 = 4x + 1
We can simplify this equation by subtracting 4y from both sides:
-3 = 4x - 4y + 4
Then we can divide both sides by 4:
x - y + 1 = 0
This is the third equation that relates x and y, based on the first and fourth sides of the square.
Now we have three equations that relate x and y. We can solve for one variable in terms of the other, and then substitute that expression into one of the other equations to eliminate one variable.
For example, we can solve the first equation for y:
3x - y = -3
y = 3x + 3
Then we can substitute this expression for y into the second equation:
x = y - 1
x = (3x + 3) - 1
x = 3x + 2
-2 = 2x
x = -1
Now we know that x is -1. We can substitute this value into one of the equations to solve for y. Let's use the second equation:
x = y - 1
-1 = y - 1
y = 0
Now we know that y is 0. We can substitute these values into any of the sides of the square to get its length, and then calculate its area.
For example, the first side is 4y - 3, which is:
4(0) - 3 = -3
The second side is 5y - 3x, which is:
5(0) - 3(-1) = 3
The third side is y + 3x, which is:
0 + 3(-1) = -3
The fourth side is 4x + 1, which is:
4(-1) + 1 = -3
Since all four sides are equal in length (and they are all equal to -3), the square has side length of 3. Its area is therefore:
area = 3^2 = 9
I hope that explains it better!
- 4y - 3
- 5y - 3x
- y + 3x
- 4x + 1
We know that all four sides of a square are equal in length. So we take any two sides and set them equal to each other, and then we can solve for the values of x and y that make them equal.
For example, let's take the first two sides and set them equal:
4y - 3 = 5y - 3x
We can simplify this equation by subtracting 4y from both sides:
-3 = y - 3x
Then we can add 3x to both sides:
3x - y = -3
This is one equation that relates x and y, based on the first two sides of the square. We can do the same thing with any two sides to get another equation.
If we set the first and third sides equal:
4y - 3 = y + 3x
We can simplify this equation by subtracting y from both sides:
3y - 3 = 3x
Then we can divide both sides by 3:
x = y - 1
This is another equation that relates x and y, based on the first and third sides of the square. If we set the first and fourth sides equal, we get another equation:
4y - 3 = 4x + 1
We can simplify this equation by subtracting 4y from both sides:
-3 = 4x - 4y + 4
Then we can divide both sides by 4:
x - y + 1 = 0
This is the third equation that relates x and y, based on the first and fourth sides of the square.
Now we have three equations that relate x and y. We can solve for one variable in terms of the other, and then substitute that expression into one of the other equations to eliminate one variable.
For example, we can solve the first equation for y:
3x - y = -3
y = 3x + 3
Then we can substitute this expression for y into the second equation:
x = y - 1
x = (3x + 3) - 1
x = 3x + 2
-2 = 2x
x = -1
Now we know that x is -1. We can substitute this value into one of the equations to solve for y. Let's use the second equation:
x = y - 1
-1 = y - 1
y = 0
Now we know that y is 0. We can substitute these values into any of the sides of the square to get its length, and then calculate its area.
For example, the first side is 4y - 3, which is:
4(0) - 3 = -3
The second side is 5y - 3x, which is:
5(0) - 3(-1) = 3
The third side is y + 3x, which is:
0 + 3(-1) = -3
The fourth side is 4x + 1, which is:
4(-1) + 1 = -3
Since all four sides are equal in length (and they are all equal to -3), the square has side length of 3. Its area is therefore:
area = 3^2 = 9
I hope that explains it better!