Latest Elitmus Aptitude Question SOLUTION: D and E are the midpoints of AB and AC of triangle ABC; BC is produced to any point P;DE , DP & EP are joined, then 1. trng PED=1/4TRNG ABC 2.TRNG PED =TRNG BEC 3. TRNG ADE =TRNG

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(#M40152455) ELITMUS Numerical Ability question geometry Keep an EYE

D and E are the midpoints of AB and AC of triangle ABC; BC is produced to any point P;DE , DP & EP are joined, then
1. trng PED=1/4TRNG ABC
2.TRNG PED =TRNG BEC
3. TRNG ADE =TRNG BEC
4. TRNG BDE = TRNG BEC

Asked In Elitmus shankey (8 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

Kunal Wadhwa  (8 years ago)

In triangle ABC, D is mid point of AB and E is mid point of AC (Given)
AD / AB = AE / AC = 1/2 ................................................................... (i)
so Triangle ADE is similar to Triangle ABC
thus => area of tri (ADE) / area of tri (ABC) = AD2 / AB2 = 1/4 (from (i)).............................. (ii)

Now you have to do some construction
Draw perpendicular from E to BC and name the intersection point as F
Similarly Draw perpendicular from E until point A and name that point as G
Now Triangle AGE is similar to Triangle EFC (as 2 angles are equal)
so AE/EC = EG/EF = 1
EG = EF ...................................................... (iii)
area (tri DEP) = 1/2 * DE * EF
area (tri ADE) = 1/2 *DE * GE
From eq (iii)
area (tri DEP) = area (tri ADE) .......................... (iv)
thus using eq (ii)
area (tri DEP) = 1/4 area(tri ABC)

Is this solution Helpfull? Yes (13) | No (4)  

Kaustabh Bhattacharya  (8 years ago)

Ans 1 draw the pic u ll get

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kundan prasad  (8 years ago)

Ans: 1
after drawing the picture, we get the 5 eqiualteral triangle

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D.RAVIKIRAN  (8 years ago)

can sme please explain the answer properly ?

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akash  (8 years ago)

plz explain it..

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yashwant  (8 years ago)

if u will take triangle as an equilateral triangle and p as a mid point of bc .then it will become easy to solve .ans is 1.

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SANTU MAITY  (8 years ago)

option (1) trng PED=1/4 trng ABC

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