angle AED congruent angle ABC, AD = 3 , DB = 5 AE = 4 then the length of AC is
A)2
B)6
C)8
D)12
Answers
If Angle AED congruent angle ABC, AD = 3 , DB = 5 AE = 4 then the length of AC is option (B): 6.
Step-by-step explanation:
Referring to the figure attached below, consider ∆AED and ∆ABC, we have
∠AED = ∠ABC ….. (given)
∠A = ∠A …… (common angle)
∴ By AA similarity, ∆AED ~ ∆ABC
We know that the corresponding sides of two similar triangles are proportional to each other.
∴ AE/AB = AD/AC
⇒ AE/(AD+DB) = AD/AC
Substituting the given values of AE=4, AD=3, DB=5
⇒ 4/(3+5) = 3/AC
⇒ 4/8 = 3/AC
⇒ ½ = 3/AC
⇒ AC = 6
Thus, the length of AC is 6.
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