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

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**.

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