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Question

In fig 1.40, ABC is right-angled at B.
D is any point on AB and seg DE seg AC.
If AD=6 cm, AB=12 cm and AC=18 cm, find AE.

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Solution

In ABC andAED,ABCAED (90° each)BACEAD (Common angle )Therefore, by the AA similarity test, ABC~AED.Hence, by the property of similarity,ABAE=ACAD12AE=186AE=12×618=4 cm

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