Question
Given that ABCD is a rectangle with AO = 4x - 3 and BO = 5x - 10, what is the value
of x?
of x?
Answers
GPT-4o mini
In a rectangle, the diagonals are equal in length. In the case of rectangle ABCD, let the points A, B, C, and D be such that A is at one vertex, B is at an adjacent vertex, and O is the midpoint of diagonal AC.
The lengths AO and BO are given as:
- \( AO = 4x - 3 \)
- \( BO = 5x - 10 \)
Since O is the midpoint of the diagonals, we have the property that the lengths of AO and BO must be equal.
Setting the two expressions equal to each other, we have:
\[
4x - 3 = 5x - 10
\]
Now, we can solve for \( x \):
1. Rearrange the equation to isolate \( x \):
\[
4x - 5x = -10 + 3
\]
\[
-x = -7
\]
2. Multiply both sides by -1 to solve for \( x \):
\[
x = 7
\]
Thus, the value of \( x \) is \( \boxed{7} \).
The lengths AO and BO are given as:
- \( AO = 4x - 3 \)
- \( BO = 5x - 10 \)
Since O is the midpoint of the diagonals, we have the property that the lengths of AO and BO must be equal.
Setting the two expressions equal to each other, we have:
\[
4x - 3 = 5x - 10
\]
Now, we can solve for \( x \):
1. Rearrange the equation to isolate \( x \):
\[
4x - 5x = -10 + 3
\]
\[
-x = -7
\]
2. Multiply both sides by -1 to solve for \( x \):
\[
x = 7
\]
Thus, the value of \( x \) is \( \boxed{7} \).