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Lines AC¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯ are diagonals of ABCD . What value of x makes ABCD a rectangle if AC=x+7 and BD=3x−5 ? (1 point) Responses x=6 x equals 6 x=13 x equals 13 x=15 x equals 15 x=8

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For quadrilateral ABCD to be a rectangle, its diagonals AC and BD must be equal in length. Therefore, we can set up the equation:

\[ AC = BD \]

Substituting the expressions given:

\[ x + 7 = 3x - 5 \]

Now, we'll solve for \( x \):

  1. Subtract \( x \) from both sides:

\[ 7 = 2x - 5 \]

  1. Add 5 to both sides:

\[ 12 = 2x \]

  1. Divide both sides by 2:

\[ x = 6 \]

Thus, the value of \( x \) that makes ABCD a rectangle is \( x = 6 \).

So the correct response is: x = 6.