Question
The rectangle ABCD is given as shown. Find x if CO=−3x and BD=x+21
Answers
GPT 3.5
The diagonals of a rectangle bisect each other, so we know that BO is equal to DO. We can set up an equation using this information.
Since BO and DO are equal, we have:
BD = BO + OD
Substituting in the given values, we get:
x + 21 = -3x + x + 21
Combining like terms, we have:
x + 21 = -2x + 21
Adding 2x to both sides, we get:
3x + 21 = 21
Subtracting 21 from both sides, we have:
3x = 0
Dividing by 3, we find:
x = 0
Therefore, x = 0.
Since BO and DO are equal, we have:
BD = BO + OD
Substituting in the given values, we get:
x + 21 = -3x + x + 21
Combining like terms, we have:
x + 21 = -2x + 21
Adding 2x to both sides, we get:
3x + 21 = 21
Subtracting 21 from both sides, we have:
3x = 0
Dividing by 3, we find:
x = 0
Therefore, x = 0.