Question

The rectangle ABCD
is given as shown. Find x if CO=−3x
and BD=x+21
.

(1 point)
Responses

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

x=−3
x equals negative 3

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

x=3

Answer 1

To find the value of \( x \) given the geometrical conditions on the rectangle \( ABCD \), we need to recognize some properties of the rectangle and the relationships given.

Let’s denote:
- The length \( CO \) as \( -3x \)
- The length \( BD \) as \( x + 21 \)

In a rectangle, the diagonals are equal in length. Therefore, we can set the lengths equal to each other:

\[
-3x = x + 21
\]

Now, let's solve for \( x \). First, we can arrange the equation by moving \( x \) to the left side:

\[
-3x - x = 21
\]

This simplifies to:

\[
-4x = 21
\]

Now, we divide both sides by -4:

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

When expressed as a fraction, this is:

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

Now, let's compare this solution to the answer choices provided:

- \( x=−425 \)
- \( x = -\frac{42}{5} \)
- \( x=−3 \)
- \( x=−\frac{21}{4} \)
- \( x=3 \)

The correct answer is:

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