Question

In the given figure, ABCD is a rectangle in which AB = 12 cm, BC = 8 cm; E is a point on BC such that BE = 5 cm. AE, when produced meets DC produced at F. (i) Calculate the length of AE. (ii) Prove that triangles ABE and FCE are similar; hence evaluate the length of EF.

Answer 1

Answer:

(i) 13cm...

Explanation :

(i) W.K.T ABE is a right angled triangle where angle B = 90 degree. By applying Pythagoras theorem we get, AE = 13cm.. (Pythagorean triplet)

(ii) In Triangle ABE and triangle ECF,

• angle B = angle C = 90 degrees
• angle AEB = angle FEC (common vertex)
• angle BAE = angle CFE (remaining angle)

therefore, triangle ABE is similar to triangle ECF (AA similarly criteria)

Hence proved