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

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

GPT-4o mini · Answer

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.**