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# In δAbc, D and E Are Points on the Sides Ab and Ac Respectively Such that De || Bc If "Ad"/"Db"=2/3 And Ac = 18 Cm, Find Ae - Mathematics

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#### Question

In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC

If "AD"/"DB"=2/3 and AC = 18 cm, find AE

#### Solution

We have,

"AD"/"DB"=2/3and DE || BC

Therefore, by basic proportionality theorem, we have

"AD"/"DB"="EC"/"AE"

rArr3/2="EC"/"AE"

Adding 1 on both sides, we get

rArr3/2+1="EC"/"AE"+1

rArr(3+2)/2=("EC"+"AE")/"AE"

rArr5/2="AC"/"AE"               [∵ AE + EC = AC]

rArr5/2=18/"AE"                 [∵ AC = 18]

rArr"AE=(18xx2)/5"

rArr"AE"=36/5=7.2 " cm"

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#### APPEARS IN

RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.2 | Q: 1.03 | Page no. 19
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 7: Triangles
Ex. 7.2 | Q: 1.03 | Page no. 19

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Solution In δAbc, D and E Are Points on the Sides Ab and Ac Respectively Such that De || Bc If "Ad"/"Db"=2/3 And Ac = 18 Cm, Find Ae Concept: Basic Proportionality Theorem Or Thales Theorem.
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