n the square ABCD, AE = 3x + 5 and BD = 10x + 2. What is the length of modifying above upper A upper C with bar?
Square upper A upper B upper C upper D is shown with diagonals upper B upper D and upper A upper C intersecting at point upper E.
(1 point)
Responses
2
2
11
11
22
22
32
32
To find the length of modifying above upper A upper C with bar (AC'), we need to determine the length of the segment AC' by finding the difference between the lengths of AE and EC' (AE - EC').
Since ABCD is a square, AC is a diagonal of the square. Therefore, the length of AC is equal to the length of AC' (AC = AC').
Given that AE = 3x + 5, we can substitute AC' for AC in the equation AE - EC' = AC to solve for AC'.
3x + 5 - EC' = AC'
But since AC = AC', we can replace AC' with AC in the equation.
3x + 5 - EC' = AC
Now, we need to find the length of EC'. We can do this by subtracting the lengths of BD and AE from AC' and setting it equal to EC'.
AC' = AC = 3x + 5
BD = 10x + 2
AE = 3x + 5
EC' = AC' - BD - AE
EC' = (3x + 5) - (10x + 2) - (3x + 5)
EC' = 3x + 5 - 10x - 2 - 3x - 5
EC' = -10x - 2
Now, we can substitute -10x - 2 for EC' in the equation.
3x + 5 - (-10x - 2) = AC'
3x + 5 + 10x + 2 = AC'
13x + 7 = AC'
Therefore, the length of modifying above upper A upper C with bar is 13x + 7.