Question

Segment upper C upper O is labeled negative 3 x. Segment upper B upper D is labeled x plus 21.


Image Long DescriptionSegment upper C upper O is labeled negative 3 x. Segment upper B upper D is labeled x plus 21.

The rectangle ABCD
𝐴
𝐵
𝐶
𝐷
is given as shown. Find x if CO=−3x
𝐶
𝑂
=
−
3
𝑥
and BD=x+21
𝐵
𝐷
=
𝑥
+
21
.

(1 point)
Responses

x=−214
𝑥
=
−
21
4

x equals negative Start Fraction 21 over 4 End Fraction

x=3
𝑥
=
3

x equals 3

x=−425
𝑥
=
−
42
5

x equals negative Start Fraction 42 over 5 End Fraction

x=−3

Answer 1

O is the intersection of the diagonals, so CO is half of BD (diagonals of a rectangle are equal and bisect each other). Thus

-3x = (x + 21)/2.

Multiply by 2: -6x = x + 21 → -7x = 21 → x = -3.

(Check: CO = -3(-3)=9, BD = -3+21=18, and 9 = 18/2.)