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Question

A quadrilateral is labeled upper A upper B upper C upper D. A segment connects upper B and upper D. Another segment connects upper A and upper C. The point where the segments intersect is upper E.

In the rectangle BCDA
, AE¯¯¯¯¯¯¯¯
can be expressed as 3x
and ED¯¯¯¯¯¯¯¯
as −4x+21
. Identify a pattern to find the total length of BD¯¯¯¯¯¯¯¯
.

(1 point)
Responses

9
9

27
27

3
3

18

Answer 1

To solve for the total length of \( BD \) based on the given segments \( AE \) and \( ED \):

1. We have \( AE = 3x \) and \( ED = -4x + 21 \).
2. The total length of \( BD \) can be expressed as the sum of \( AE \) and \( ED \): \[ BD = AE + ED = 3x + (-4x + 21) = 3x - 4x + 21 = -x + 21 \]

Next, we need to find \( x \) to determine the total length of \( BD \). However, since the question does not provide a specific value for \( x \), we look to see if there is a pattern evident or specific values provided in the choices given.

Assuming that the problem needs us to analyze \( -x + 21 \):

1. We can set the possible values:

   • If \( x = 3 \): \[ BD = -3 + 21 = 18 \]
   • If \( x = 6 \): \[ BD = -6 + 21 = 15 \]
   • If \( x = 0 \): \[ BD = -0 + 21 = 21 \]

2. Among the answers, the closest consistent value derived from the expression \( -x + 21 \) when \( x = 3 \) gives us \( 18 \).

Therefore, based on the potential values and given the options, the total length of \( BD \) is:

18.