Question
If ABCD
is a rectangle where AC=19
and DB=3x+4
, what is the value of x?
(1 point)
Responses
x=2.25
x equals 2.25
x=12
x equals 12
x=5
x equals 5
x=10
is a rectangle where AC=19
and DB=3x+4
, what is the value of x?
(1 point)
Responses
x=2.25
x equals 2.25
x=12
x equals 12
x=5
x equals 5
x=10
Answers
GPT-4o mini
In a rectangle, the diagonals are equal. So, we can set the lengths of the diagonals equal to each other:
Given:
- Length of diagonal \( AC = 19 \)
- Length of diagonal \( DB = 3x + 4 \)
We can set up the equation:
\[
19 = 3x + 4
\]
Now, we'll solve for \( x \):
1. Subtract 4 from both sides:
\[
19 - 4 = 3x
\]
\[
15 = 3x
\]
2. Divide both sides by 3:
\[
x = \frac{15}{3}
\]
\[
x = 5
\]
Thus, the value of \( x \) is \( 5 \).
The answer is:
**x = 5**.
Given:
- Length of diagonal \( AC = 19 \)
- Length of diagonal \( DB = 3x + 4 \)
We can set up the equation:
\[
19 = 3x + 4
\]
Now, we'll solve for \( x \):
1. Subtract 4 from both sides:
\[
19 - 4 = 3x
\]
\[
15 = 3x
\]
2. Divide both sides by 3:
\[
x = \frac{15}{3}
\]
\[
x = 5
\]
Thus, the value of \( x \) is \( 5 \).
The answer is:
**x = 5**.