Question

Lines AC and BD are diagonals of ABCD. What value of x makes ABCD a rectangle if AC = x + 29 and BD = 4x - 1.

a. x = 10
b. x = 12
c. x = 6
d. x = 15

Answer 1

For quadrilateral ABCD to be a rectangle, the diagonals must be equal in length. Therefore, we can set the lengths of the diagonals equal to each other:

\[
AC = BD
\]

Substituting the expressions we have for the diagonals:

\[
x + 29 = 4x - 1
\]

Now, we will solve for \( x \). First, rearrange the equation:

\[
29 + 1 = 4x - x
\]

This simplifies to:

\[
30 = 3x
\]

Now, divide both sides by 3:

\[
x = 10
\]

Thus, the value of \( x \) that makes quadrilateral ABCD a rectangle is

\[
\boxed{10}
\]