Question

In the given fig. DE || BC, AD=4 and BD=5, AC=8 then find AE.​

Answer 1

Given : DE || BC, AD=4 and BD=5, AC=8

To Find :   AE

Solution:

DE || BC

Thales theorem :

if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

=> AD/BD  = AE / EC

=> 4 / 5  = AE / EC

=> AE / EC  = 4/5

EC = AC - AE

=> EC = 8 - AE

=> AE/( 8 - AE)  = 4/5

=> 5AE = 32 - 4AE

=> 9 AE = 32

=> AE =  32/9

AE.​ =  32/9

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