Question

Given that ABCD is a rectangle with AO=4x−3 and BO=5x−10 , what is the value of x? (1 point) Responses x=−13 x equals negative 13 x=7 x equals 7 x=−43 x equals negative Start Fraction 4 over 3 End Fraction x=176

Answer 1

In a rectangle, the diagonals are equal in length. Given that \( AO \) and \( BO \) are the lengths of segments from one vertex to the opposite corner (assuming \( O \) is the midpoint of the diagonal), we can set them equal to each other:

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

Now, 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 \( 7 \).

So the answer is \( x = 7 \).