Question
Given that quadrilateral ABCD is a rectangle with AC = 5/2x and BD = 2x + 5 find the value of x.
(1 point
(1 point
Answers
GPT-4o mini
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
\[
\boxed{10}
\]
\[
AC = BD
\]
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
\[
\boxed{10}
\]