In the figure, AB = AD = 7cm and AC = AE and BC = 11 cm, then find the length of ED.
Answer & explanation
Correct answer: option 3
Since AB = AD, and AC = AE, by concept,
triangle ABC is similar to triangle ADE
Therefore, \(\frac{AB}{AD}\) = \(\frac{BC}{ED}\) = \(\frac{AC}{AE}\)
Now, \(\frac{AB}{AD}\) = \(\frac{BC}{ED}\)
⇒ 1 = \(\frac{11}{ED}\) (because AB = AD)
⇒ ED = 11,
Therefore, the length of ED is 11 cm.