Diagonal of a parallelogram

[Big Dog 04]

Q, How do you calculate it? See attachment for question. Thanks.

sdp.doc

[hello_mona]

hi bigdog,

 

first consider the point where the rt. triangle is formed as E.

 

Since its a parallelogram BC=AD=12.

 

draw a straight line from point C to AD and name it as F.

 

so, DF=CE=2 and CF=ED=4

 

so now u have AF=10, CF=4 use pythogaraeus theorem on triangle AFC ..

 

u get AC as sqrt(116) = 2sqrt(29)

[coolpaggy]

hi big dog 4 !!

here is the solution for the Q u asked. its quite simple all u need to do is to drop an extra perpandicular...see, I've put it up in the following attachment... :tup:

parallogram_solution.doc

[Big Dog 04]

@Thank you very much both of u - you are right it is an easy question once you insert the perpendicular!! Much appreciated. BD

[Commentor]

You can avoid that extra perpendicular,

if you remember that

 

|AB|^2 + |BC|^2 + |CD|^2 +|DA|^2 = |AC|^2 + |BD|^2 for

a parallelogram ABCD.

[manasi4gre]

commentor,but i got 2sqrt(41) using AB^2 + BC^2 + CD^2 + DA^2=AC^2 + BD^2....it doesnt match with the ans. drawn by dropping the perpendicular

i.e. 2sqrt(29)

[coolpaggy]

commentor,but i got 2sqrt(41) using AB^2 + BC^2 + CD^2 + DA^2=AC^2 + BD^2....it doesnt match with the ans. drawn by dropping the perpendicular

i.e. 2sqrt(29)

 

Mansi please open the attachment I have uploaded. It'll clear all your doubts. (ale ka laxat ata tari ?) :grad:

[hello_mona]

yea commentor..can u pls clarify tht?? coz even i am not getting 2sqrt(29) by using tht method.

[manasi4gre]

Mansi please open the attachment I have uploaded. It'll clear all your doubts. (ale ka laxat ata tari ?) :grad:

 

parag,

I solved this problem by dropping an extra perpendicular to get the ans. as

2sqrt(29) exactly like the way you did. But i dont seem to get the same ans. applying AB^2 + BC^2 + CD^2 + DA^2=AC^2 + BD^2....the ans. is 2sqrt(41).

 

 

can you clarify the reason for the two different answers ,commentor?

 

 

p.s: parag,what do you mean by "ale ka laxat ata tari ?"

[coolpaggy]

parag,

I solved this problem by dropping an extra perpendicular to get the ans. as

2sqrt(29) exactly like the way you did. But i dont seem to get the same ans. applying AB^2 + BC^2 + CD^2 + DA^2=AC^2 + BD^2....the ans. is 2sqrt(41).

 

 

can you clarify the reason for the two different answers ,commentor?

 

 

p.s: parag,what do you mean by "ale ka laxat ata tari ?"

 

I request you to open the attachment I have uploaded in my solution. Please refer to it so no doubts could persist.

 

PS : "ale ka laxat" means, did you undertand now ???