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

Question

(1 point)
x = - 4/3
x = - 13
x = 7
x = 17/6

Answer 1

In a rectangle, the length of the diagonals are equal. Hence, we can set \( AO \) equal to \( BO \):

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

To solve for \( x \), we first rearrange the equation:

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

This simplifies to:

\[ -x = -7 \]

Multiplying both sides by -1 gives us:

\[ x = 7 \]

So, the value of \( x \) is \( 7 \).

The answer is \( x = 7 \).