Question

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

x=-42/5
x=-21/4
x=-3
x=3

Answer 1

To solve for \( x \) in the rectangle ABCD with the given segments CO and BD, we need to analyze the relationship between these lengths.

1. **Identify Segments**:
- CO = -3x
- BD = x + 21

2. **Length of Diagonal in Rectangle**:
In a rectangle, the diagonals are equal. Therefore, we set \( CO \) equal to \( BD \):
\[
-3x = x + 21
\]

3. **Solve for \( x \)**:
Rearranging the equation to isolate \( x \):
\[
-3x - x = 21
\]
\[
-4x = 21
\]
\[
x = -\frac{21}{4}
\]

Thus, the value of \( x \) is \(\boxed{-\frac{21}{4}}\). This matches one of the provided options.