Question

The rectangle ABCD
𝐴
𝐵
𝐶
𝐷
is given as shown. Find x if CO=−3x
𝐶
𝑂
=
−
3
𝑥
and BD=x+21
𝐵
𝐷
=
𝑥
+
21
.

(1 point)
Responses

x=−425
𝑥
=
−
42
5
x equals negative Start Fraction 42 over 5 End Fraction

x=−3
𝑥
=
−
3
x equals negative 3

x=−214
𝑥
=
−
21
4
x equals negative Start Fraction 21 over 4 End Fraction

x=3

Answer 1

To find \( x \) based on the provided equations \( CO = -3x \) and \( BD = x + 21 \), we can utilize the properties of a rectangle.

In a rectangle, the diagonals are equal in length. This means that \( BD \) (the length of diagonal \( BD \)) must equal \( CO \) (the length of diagonal \( CO \)). Therefore, we can set up the equation:

\[
-3x = x + 21
\]

Now, let's solve for \( x \).

1. First, we can add \( 3x \) to both sides of the equation:

\[
-3x + 3x = x + 3x + 21
\]

This simplifies to:

\[
0 = 4x + 21
\]

2. Next, we can subtract \( 21 \) from both sides:

\[
-21 = 4x
\]

3. Finally, we divide by \( 4 \):

\[
x = -\frac{21}{4}
\]

Thus, the value of \( x \) is

\[
\boxed{-\frac{21}{4}}
\]

So the correct choice from your listed responses would be:

\( x = -\frac{21}{4} \)