Question
Given that ABCD is a rectangle with AO=4x-3 and BO=5x-10, what is the value of x?
X=7
X= -4/3
X=17/6
X= -13
X=7
X= -4/3
X=17/6
X= -13
Answers
GPT-4o mini
In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths of the diagonals \( AO \) and \( BO \) equal to each other:
\[
AO = BO
\]
Given:
\[
AO = 4x - 3
\]
\[
BO = 5x - 10
\]
Setting these equal, we have:
\[
4x - 3 = 5x - 10
\]
To solve for \( x \), first isolate \( x \) by subtracting \( 4x \) from both sides:
\[
-3 = x - 10
\]
Next, add \( 10 \) to both sides:
\[
-3 + 10 = x
\]
This simplifies to:
\[
x = 7
\]
Thus, the value of \( x \) is \( \boxed{7} \).
\[
AO = BO
\]
Given:
\[
AO = 4x - 3
\]
\[
BO = 5x - 10
\]
Setting these equal, we have:
\[
4x - 3 = 5x - 10
\]
To solve for \( x \), first isolate \( x \) by subtracting \( 4x \) from both sides:
\[
-3 = x - 10
\]
Next, add \( 10 \) to both sides:
\[
-3 + 10 = x
\]
This simplifies to:
\[
x = 7
\]
Thus, the value of \( x \) is \( \boxed{7} \).