ABCD is a rectangle. If AC=5x+2 and BD=x+22, find x.
In a rectangle, the diagonals are equal. So,
5x+2 = x+22
4x = 20
x = 5
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Since ABCD is a rectangle, its opposite sides are equal in length.
Given that AC = 5x + 2 and BD = x + 22, we can set up an equation:
AC = BD
5x + 2 = x + 22
To solve for x, we need to isolate it on one side of the equation.
First, let's subtract x from both sides:
5x + 2 - x = x + 22 - x
4x + 2 = 22
Next, let's subtract 2 from both sides:
4x + 2 - 2 = 22 - 2
4x = 20
To solve for x, divide both sides by 4:
4x/4 = 20/4
x = 5
Therefore, x = 5.
To find the value of x, we need to use the properties of a rectangle.
In a rectangle, opposite sides are equal. In this case, AC is opposite to BD, so AC = BD.
Given that AC = 5x+2 and BD = x+22, we can set up the equation:
5x+2 = x+22
To solve for x, we need to isolate the variable on one side of the equation.
Let's solve the equation step-by-step:
1. Start with the equation: 5x+2 = x+22
2. First, subtract x from both sides of the equation to remove the variable from the right side:
5x - x + 2 = x - x + 22
This simplifies to:
4x + 2 = 22
3. Next, subtract 2 from both sides of the equation:
4x + 2 - 2 = 22 - 2
This simplifies to:
4x = 20
4. Divide both sides of the equation by 4 to solve for x:
(4x)/4 = 20/4
This simplifies to:
x = 5
Therefore, the value of x is 5.