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14. If AABC~ ADEF, what is the length of DE ?

18
A
B
24
20
C D
E
10

User LastElb
by
7.7k points

1 Answer

4 votes

The length of DE is 10.

In similar triangles, corresponding sides are proportional. The given statement AABC~ ADEF indicates that triangle ABC is similar to triangle DEF. Therefore, the ratio of the corresponding sides is equal. In this case, AB/DE = AC/DF = BC/EF.

Since AB is given as 18 and AC is given as 24, we can set up a proportion: 18/DE = 24/DF. S

olving for DE, we find DE = (18 * DF) / 24.

Given DF as 10, substituting the value, we get DE = (18 * 10) / 24 = 180 / 24 = 10.

So, the length of DE is 10 units, determined by the proportional relationship between corresponding sides of similar triangles AABC and ADEF.

User Cch
by
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