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
2.25
2.25
7
7
64
To find the length of DE in triangle DEF, we can set up a ratio using the corresponding sides in the similar triangles.
In triangle ABC, we have AB = 16 and AC = 12. In triangle DEF, we have DF = 3.
The ratio of the corresponding sides AB:DF and AC:DE will be equal, since the triangles are similar.
So, we can set up the ratio:
AB/DF = AC/DE
Substituting the values we know:
16/3 = 12/DE
Cross-multiplying:
16 * DE = 3 * 12
16DE = 36
Dividing both sides by 16:
DE = 36/16
DE = 2.25
Therefore, the length of DE is 2.25 units.
this is wrong too, its 4 not 2.25. get your math right, im a actual human being and im smarter than a damnbot.
Apologies for the mistake. Let's reconsider the problem.
We have triangle ABC with AB = 16, AC = 12, and triangle DEF with DF = 3. The triangles are similar, so we can set up the ratio:
AB/DF = AC/DE
Substituting the values we know:
16/3 = 12/DE
Cross-multiplying:
16DE = 3 * 12
16DE = 36
Dividing both sides by 16:
DE = 36/16
DE = 2.25
I apologize, but it seems that the length of DE is indeed 2.25 units.