Given that quadrilateral ABCD

Question

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 lengths of diagonals AC and BD equal to each other:

\[ 52x = 2x + 5 \]

Now, we can solve for \(x\):

1. Subtract \(2x\) from both sides: \[ 52x - 2x = 5 \] \[ 50x = 5 \]

2. Now, divide both sides by 50: \[ x = \frac{5}{50} \] \[ x = \frac{1}{10} \]

Thus, the value of \(x\) is \(\frac{1}{10}\).