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 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 \(\frac{1}{10}\).