Question

The rectangle ABCD is given as shown. Find x if CO=−3x and BD=x+21 . (1 point) Responses x=−214 x equals negative Start Fraction 21 over 4 End Fraction x=3 x equals 3 x=−3 x equals negative 3 x=−425 x equals negative Start Fraction 42 over 5 End Fraction

Answer 1

To find the value of \( x \), we start by understanding the geometric relationships in rectangle ABCD.

1. In a rectangle, the diagonals are equal in length. Therefore, we have:
\[
CO = BD
\]

2. From the problem statement:
\[
CO = -3x
\]
\[
BD = x + 21
\]

3. Setting the two expressions for the lengths of the diagonals equal gives us the equation:
\[
-3x = x + 21
\]

4. To solve for \( x \), we will first move all the terms involving \( x \) to one side of the equation:
\[
-3x - x = 21
\]
\[
-4x = 21
\]

5. Next, we divide both sides by -4 to solve for \( x \):
\[
x = \frac{21}{-4}
\]
\[
x = -\frac{21}{4}
\]

Thus, the solution is:
\[
x = -\frac{21}{4}
\]

Looking at the provided responses, the final answer matches with:
**x equals negative Start Fraction 21 over 4 End Fraction**.