Question

Given that quadrilateral ABCD is a rectangle with AC = 5/2x and BD = 2x + 5 value of x.

x = _

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, we have:

\[
AC = BD
\]

Given that:
\[
AC = \frac{5}{2}x \quad \text{and} \quad BD = 2x + 5
\]

We can set the two expressions for the diagonals equal to each other:

\[
\frac{5}{2}x = 2x + 5
\]

Now, let's solve for \(x\). First, we can eliminate the fraction by multiplying the entire equation by 2:

\[
5x = 4x + 10
\]

Next, we will subtract \(4x\) from both sides:

\[
5x - 4x = 10
\]
\[
x = 10
\]

Thus, the value of \(x\) is:

\[
\boxed{10}
\]