Use the image to answer the question.

A triangle marked clockwise from the left vertex as upper A upper B upper C. Congruent line segments and angles are marked.

In the figure, ΔDBE has the following side lengths: DB¯¯¯¯¯¯¯¯=12 units, BE¯¯¯¯¯¯¯¯=7 units, and DE¯¯¯¯¯¯¯¯=14 units. What is the length of AB¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

24 units
24 units

14 units
14 units

12 units
12 units

28 units
28 units
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1 answer

Based on the given information and the properties of congruent triangles, we need to determine the length of \( AB \) based on the triangle \( \Delta DBE \) with the specified side lengths.

The side lengths of triangle \( \Delta DBE \) are:

  • \( DB = 12 \) units
  • \( BE = 7 \) units
  • \( DE = 14 \) units

Since we have no specific visual reference to the triangle \( \Delta ABC \) in the question, we might rely on relational congruence. However, we can't infer any relationship between the triangles without additional information about how \( A, B, C \) correlate to \( D, E \).

If the triangles \( \Delta ABC \) and \( \Delta DBE \) are congruent (given any specific markings or angles that suggest this), the lengths of corresponding sides would be equal.

In this case, we can find that \( AB \) corresponds to \( DE \) (if \( \Delta ABC \sim \Delta DBE \)). Thus, if \( DE = 14 \) units, \( AB \) would also equal \( 14 \) units.

Therefore, the length of \( AB \) is 14 units.

So, the correct response is: 14 units

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