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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

7
7

2.25
2.25

64
64
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Answer 1

To find the length of side DE in triangle DEF, we can use the property of similar triangles.

Since triangles ΔABC and ΔDEF are similar, the ratios of the corresponding sides are equal. This means:

\[ \frac{AB}{DE} = \frac{AC}{DF} \]

We know:

• AB = 16
• AC = 12
• DF = 3

We can substitute these values into the ratio:

\[ \frac{16}{DE} = \frac{12}{3} \]

Calculating the right side:

\[ \frac{12}{3} = 4 \]

Now we have:

\[ \frac{16}{DE} = 4 \]

To find DE, we can cross-multiply:

\[ 16 = 4 \cdot DE \]

Now, solve for DE:

\[ DE = \frac{16}{4} = 4 \]

Thus, the length of DE is 4.