Question
Given that quadrilateral ABCD is a rectangle with AO=4x−3
and BO=5x−10
, find the value of x.
(1 point)
x=
and BO=5x−10
, find the value of x.
(1 point)
x=
Answers
GPT-4o mini
In a rectangle, the diagonals are equal in length. Therefore, we can set \( AO \) equal to \( BO \).
Given:
\[
AO = 4x - 3
\]
\[
BO = 5x - 10
\]
Setting them equal to each other:
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \):
1. Subtract \( 4x \) from both sides:
\[
-3 = x - 10
\]
2. Add \( 10 \) to both sides:
\[
7 = x
\]
Thus, the value of \( x \) is:
\[
\boxed{7}
\]
Given:
\[
AO = 4x - 3
\]
\[
BO = 5x - 10
\]
Setting them equal to each other:
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \):
1. Subtract \( 4x \) from both sides:
\[
-3 = x - 10
\]
2. Add \( 10 \) to both sides:
\[
7 = x
\]
Thus, the value of \( x \) is:
\[
\boxed{7}
\]