A rectangle upper A upper B upper C upper D has diagonals between upper A upper C and upper B upper D. The diagonals insect at upper O, in the center. Diagonal upper A upper C is labeled 5-halves x. Diagonal upper B upper C is labeled 2 x plus 5.

Question

Given that quadrilateral ABCD is a rectangle with AC=52x and BD=2x+5 , find the value of x.

(1 point)
x=

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, we can set the two given diagonals equal to each other:

\[ AC = BD \]

Given that \(AC = 52x\) and \(BD = 2x + 5\), we can write the equation:

\[ 52x = 2x + 5 \]

Now, let's solve for \(x\):

1. Subtract \(2x\) from both sides:

\[ 52x - 2x = 5 \]

\[ 50x = 5 \]

2. Divide both sides by 50:

\[ x = \frac{5}{50} \]

\[ x = \frac{1}{10} \]

Thus, the value of \(x\) is

\[ \boxed{\frac{1}{10}} \]