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
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
Answers
GPT-4o mini
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**
- \( AC = x + 7 \)
- \( BD = 3x - 5 \)
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**