In the figure, AB = AD = 7 cm and AC = AE and BC = 11 cm, then find the length of ED.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 11.
AB = AD = 7 cm and AC = AE and BC = 11 cm
According to the concept of Similarity, if the two sides of a triangle are in the same proportion as the two sides of another triangle, and the angle inscribed by the two sides in both triangles are equal, then two triangles are said to be similar.
Since AB = AD, and AC = AE, according to the concept,
△ABC ~ △ADE
Hence, AB/AD = BC/ED = AC/AE
Now, AB/AD = BC/ED
= 1 = 11/ED ( AB = AD)
⇒ ED = 11
The length of ED is 11 cm.