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

Question

(1 point

Answer 1

In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals AC and BD equal to each other:

\[ AC = BD \]

Substituting the given expressions for AC and BD:

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

Now, to solve for \(x\), we first eliminate the fraction by multiplying the entire equation by 2:

\[ 5x = 4x + 10 \]

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

\[ 5x - 4x = 10 \]

This simplifies to:

\[ x = 10 \]

Thus, the value of \(x\) is

\[ \boxed{10} \]