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

Question

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

\[ \boxed{10} \]