Use the image to answer the question.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)Responsesx=13x equals 13x=15x equals 15x=6x equals 6x=8

Answer 1

To determine the value of \(x\) that makes \(ABCD\) a rectangle, we need to recognize that the diagonals of a rectangle are equal in length.

We are given:

• The length of diagonal \(AC\) as \(x + 7\).
• The length of diagonal \(BD\) as \(3x - 5\).

Setting the lengths of diagonals equal gives us the equation:

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

Now, we solve for \(x\):

1. Rearranging the equation to isolate \(x\): \[ 7 + 5 = 3x - x \] \[ 12 = 2x \]

2. Dividing both sides by 2: \[ x = 6 \]

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

The correct response is: x equals 6.