Question

witch one is right
Use the image to answer the question.

A parallelogram with vertices upper A upper B upper C upper D.

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=15
x equals 15

x=8
x equals 8

x=13

Answer 1

To determine the value of \( x \) that makes the parallelogram \( ABCD \) a rectangle, we need to know that the diagonals of a rectangle are equal in length. The given lengths of the diagonals are:

- \( AC = x + 7 \)
- \( BD = 3x - 5 \)

Setting these two expressions equal because the diagonals must be the same length in a rectangle, we have:

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

Now, let's solve for \( x \).

1. Start by subtracting \( x \) from both sides:

\[
7 = 2x - 5
\]

2. Next, add \( 5 \) to both sides:

\[
12 = 2x
\]

3. Finally, divide both sides by \( 2 \):

\[
x = 6
\]

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

The correct response is:

**x=6**
**x equals 6**