Question
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
Answers
GPT-4o mini
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**.
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**.