In rectangle ABCD, AC= 8x-10 and BD=2x+20. Find the length of BD
since AC=BD,
8x-10 = 2x+20
Now solve for x and evaluate BD=2x+20
To find the length of BD, we can use the given equation AC = 8x - 10 and BD = 2x + 20.
In a rectangle, the opposite sides are equal in length. Therefore, AC = BD.
So, we can write the equation: 8x - 10 = 2x + 20.
To solve this equation for x, we need to isolate the variable.
First, let's simplify the equation by subtracting 2x from both sides:
8x - 2x - 10 = 2x - 2x + 20.
This simplifies to: 6x - 10 = 20.
Next, let's isolate the variable by adding 10 to both sides:
6x - 10 + 10 = 20 + 10.
This simplifies to: 6x = 30.
To solve for x, divide both sides of the equation by 6:
(6x)/6 = 30/6.
This simplifies to: x = 5.
Now that we have the value of x, we can substitute it back into the equation for BD:
BD = 2x + 20.
Substituting x = 5, we get:
BD = 2(5) + 20.
This simplifies to: BD = 10 + 20 = 30.
Thus, the length of BD is 30 units.