Aadarsh
PQRS is a kite. PQ = 7, QR = 11, QS = 10. M is the mid-pint of PR. Find QM^2.
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Ishaan94
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Can you draw a figure?
Aadarsh
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Sure. Please wait.
Aadarsh
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|dw:1334216371667:dw|
apoorvk
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|dw:1334216398007:dw|
M is mid pt of PR or QS??
lgbasallote
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if QS = 10 then QM = 5
5^2 is 25
right?
Aadarsh
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@lgbasallote , u r wrong.
Aadarsh
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M is mid-point of PR.
Aadarsh
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I have done the answer, shall I post it? Will u correct it?
lgbasallote
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ahhh found it now >:))
thushananth01
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\[\frac{\sqrt{24}+\sqrt{96}}{2}\]
Aadarsh
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Wrong again.
thushananth01
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that is equal to PM
apoorvk
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Okay let me think good one. lol.
Done.|dw:1334216749935:dw|
wait let me type
thushananth01
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Cos rule i guess...what is QRM=
thushananth01
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sorry QPM?
Aadarsh
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QPM is not given.
lgbasallote
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let midpoint of QS = A
sqrt (11^2 - 5^2) = AR
AR = sqrt (121-25)
AR = sqrt (96)
AR = 4 sqrt (6)
PM + AR = PR + MA
PM = PR/2
PR/2 + 4 sqrt 6 = PR + MA
lol =)))
thushananth01
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so v can find it using sin x = 5/7
Aadarsh
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Shall I say how I did? Please. then u will check and rectify me.
thushananth01
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ok?
apoorvk
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yeah aadarsh post i am not in the patient mood to type such long replies right now.
Aadarsh
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Just a minute.
thushananth01
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answer is 31 = QM^2= 32
thushananth01
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31*
Aadarsh
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How u did @thushananth01 ? Can u say the reason please? U r absolutely right.
thushananth01
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ok first find the full length of PR
u can do this first by using pythagoras theorom
then u have to add both and divide by 2 to get the midpoint
as i gve previous with the radical..that was the length from P to M
now we know PM and PQ plus the angle QPM v can find using the sin rule then i got the angle as 45.6
then finally the cose rule\[p^{2}= q^{2} + m^{2} - 2qm (cos P)\]
\[7^{2}+7.35^{2} - 2 \times 7 \times 7.35 \cos 45.6 = p^{2}\rightarrow QM^2\]
thushananth01
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\[\frac{\sqrt{24} +\sqrt{96}}{2}\rightarrow PM\]
Aadarsh
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Thanks yaar.
thushananth01
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np :)