Question
if ABCD is a rectangle where AC=19 and DB=3x+4, what is the value of x?
Answers
GPT-4o mini
In a rectangle, the diagonals are equal in length. Therefore, we have:
\[
AC = DB
\]
Given that \( AC = 19 \) and \( DB = 3x + 4 \), we can set up the equation:
\[
19 = 3x + 4
\]
Now, solve for \( x \):
1. Subtract 4 from both sides:
\[
19 - 4 = 3x
\]
\[
15 = 3x
\]
2. Divide both sides by 3:
\[
x = \frac{15}{3} = 5
\]
Thus, the value of \( x \) is:
\[
\boxed{5}
\]
\[
AC = DB
\]
Given that \( AC = 19 \) and \( DB = 3x + 4 \), we can set up the equation:
\[
19 = 3x + 4
\]
Now, solve for \( x \):
1. Subtract 4 from both sides:
\[
19 - 4 = 3x
\]
\[
15 = 3x
\]
2. Divide both sides by 3:
\[
x = \frac{15}{3} = 5
\]
Thus, the value of \( x \) is:
\[
\boxed{5}
\]