Use the image to answer the question.

Question

An illustration shows a bigger triangle upper A upper B upper C and a smaller triangle upper D upper E upper F, with labeled sides. On the first triangle, side upper B upper C is the base and is not labeled, side upper A upper B is the hypotenuse labeled as 16, and vertical side upper A upper C on the left is labeled as 12. On the second triangle, side upper E upper F is the base and is not labeled, side upper D upper E is the hypotenuse labeled as x, and vertical side upper D upper F is on the left labeled as 3.

If ΔABC is similar to ΔDEF, and AB=16, DF=3, and AC=12, what is the length of DE?

(1 point)
Responses

4
4

64
64

7
7

2.25
2.25
Skip to navigation

page 13 of 13

Answer 1

Since the triangles ΔABC and ΔDEF are similar, their corresponding sides are proportional.

Using the proportion:

AB/DE = AC/DF

Substituting the given values:

16/DE = 12/3

Cross-multiplying:

3(16) = 12(DE)

48 = 12(DE)

Dividing both sides by 12:

4 = DE

Therefore, the length of DE is 4.