Question

Given that ABCD is a rectangle with AO=4x-3 and BO=5x-10, what is the value of x?

x=-13
x=17/6
x=-4/3
x=7

Answer 1

In rectangle ABCD, let's denote the lengths as follows:

- AO (which we'll take as the length of one side) = \( 4x - 3 \)
- BO (which we'll take as the length of the adjacent side) = \( 5x - 10 \)

In a rectangle, opposite sides are equal. Therefore, if AO and BO are lengths from one vertex to the two adjacent vertices, then they must be equal in the case where we have the diagonal or we can relate their values through the properties at play.

However, upon reviewing, it seems we don't have explicit relationships through equality but we can set the lengths through comparison to get to the value of \(x\).

Since it's a rectangle, let's set the lengths equal as they meet at the square's property that they must through proportionality reflect accordingly when set together yielding:

\[
4x - 3 = 5x - 10
\]

To solve this equation for \(x\):

1. Subtract \(4x\) from both sides:

\[
-3 = x - 10
\]

2. Add \(10\) to both sides:

\[
7 = x
\]

Thus, after isolating \(x\), we find:

**The value of \( x \) is \( 7 \)**.

Therefore, the answer is:

\[
\boxed{7}
\]