Question
Use the image to answer the question.The rectangle ABCD is given as shown. Find x if CO=−3x and BD=x+21 .(1 point)Responsesx=−214x equals negative Start Fraction 21 over 4 End Fractionx=−425x equals negative Start Fraction 42 over 5 End Fractionx=−3x equals negative 3x=3
Answers
GPT-4o mini
To find the value of \( x \) in the rectangle \( ABCD \) where \( CO = -3x \) and \( BD = x + 21 \), we can take advantage of the properties of rectangles.
In a rectangle, the diagonals are equal in length. Hence, we can set the lengths of the diagonals \( CO \) and \( BD \) equal to each other:
\[
-3x = x + 21
\]
Now, let's solve for \( x \):
1. Add \( 3x \) to both sides:
\[
0 = 4x + 21
\]
2. Subtract \( 21 \) from both sides:
\[
-21 = 4x
\]
3. Divide both sides by \( 4 \):
\[
x = -\frac{21}{4}
\]
Therefore, the value of \( x \) is
\[
x = -\frac{21}{4}
\]
Thus, the correct answer is:
**x equals negative Start Fraction 21 over 4 End Fraction.**
In a rectangle, the diagonals are equal in length. Hence, we can set the lengths of the diagonals \( CO \) and \( BD \) equal to each other:
\[
-3x = x + 21
\]
Now, let's solve for \( x \):
1. Add \( 3x \) to both sides:
\[
0 = 4x + 21
\]
2. Subtract \( 21 \) from both sides:
\[
-21 = 4x
\]
3. Divide both sides by \( 4 \):
\[
x = -\frac{21}{4}
\]
Therefore, the value of \( x \) is
\[
x = -\frac{21}{4}
\]
Thus, the correct answer is:
**x equals negative Start Fraction 21 over 4 End Fraction.**