Question

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

Answer 1

To solve for \( x \) in rectangle \( ABCD \), we can use the properties of rectangles. In a rectangle, the diagonals intersect at their midpoints, which means \( O \) is the midpoint of both diagonals \( AC \) and \( BD \).

Given:
- \( CO = -3x \)
- \( BD = x + 21 \)

Since \( O \) is the midpoint of diagonal \( BD \), the lengths \( BO \) and \( OD \) are equal, and:
\[
BD = 2 \times BO = 2 \times CO
\]

This means we can express the length of diagonal \( BD \) in terms of \( CO \) as follows:
\[
BD = 2(-3x) = -6x
\]

Now, we can set our two expressions for \( BD \) equal to each other:
\[
-6x = x + 21
\]

Next, we will solve the equation for \( x \):
\[
-6x - x = 21
\]
\[
-7x = 21
\]
\[
x = \frac{21}{-7}
\]
\[
x = -3
\]

Thus, the value of \( x \) is:
\[
\boxed{-3}
\]

Answer 2

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