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

(1 point)
x = 3
x = - 3
x = - 21/4
x = - 42/5

1 answer

To solve this problem, let's analyze the given relationships between the segments CO and BD.

We have:

  • CO = -3x
  • BD = x + 21

In a rectangle, the diagonal BD and the segments CO (which likely refers to a segment connecting the center of the rectangle to a vertex) can be related. In a rectangle, the diagonals are equal in length. If we consider CO as the length from the center O of the rectangle to the corner C, we will need more information about the positions of points A, B, C, D, and O to equate the two expressions.

However, under a typical rectangle configuration, it's common to consider both segments as part of the triangle formed by the rectangle's corners and its center. Without loss of generality, let's assume O is the midpoint of BD.

Set the two expressions equal to each other (since CO would relate to half of BD if O is the midpoint):

\[ -3x = x + 21 \]

Now, solve this equation for x:

  1. Add 3x to both sides: \[ 0 = 4x + 21 \]

  2. Subtract 21 from both sides: \[ -21 = 4x \]

  3. Divide by 4: \[ x = -\frac{21}{4} \]

Thus, the solution is \( x = -\frac{21}{4} \).

Final answer: x = -21/4.