Asked by jose
In triangle ABC, AB = 12, AC= 9, D is a point on AC, AD = 3. E is a point on AB, so that triangle ADE is similar to ABC, what is the length of AE? (two different answers)
Answers
Answered by
Reiny
Using the standard notation of listing similar triangles by listing the order of matching vertices,
triangle ADE is similar to ABC
(i.e. angle A matches with angle A, angle D matches with angle B, angle E matches with angle C, that way all ratios can be easily stated)
AE/AD = AC/AB
AE/3 = 9/12
AE = 27/12 = 9/4
or
AED is similar to ABC
AE/AB = AD/AC
AE/12 = 3/9
AE = 36/9 = 4
triangle ADE is similar to ABC
(i.e. angle A matches with angle A, angle D matches with angle B, angle E matches with angle C, that way all ratios can be easily stated)
AE/AD = AC/AB
AE/3 = 9/12
AE = 27/12 = 9/4
or
AED is similar to ABC
AE/AB = AD/AC
AE/12 = 3/9
AE = 36/9 = 4
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