Use the image to answer the 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
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page 13 of 13
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.