In the figure, AB = AD = 7cm and AC = AE and BC = 11 cm, then find the length of ED.

11

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.