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
64
64
2.25
2.25
4
4
7
The correct answer is 7.
Since ΔABC is similar to ΔDEF, the corresponding sides are proportional. Therefore, we can set up a proportion to find the length of DE.
AB/DF = AC/DE
Substituting the given values, we have:
16/3 = 12/DE
Cross-multiplying, we get:
16 * DE = 3 * 12
Simplifying, we find that DE = 7.