There Is A Square ABCD, A Point P Is On Side BC Such That P Is Mid-Point Of BC. Q Is A Point On CD, Such That Q Is One-Third Of CD. The Area Of APCQ is 108 m^2. Find The Length Of AC.
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Answers
Answer:
We know that ABCD is a square and P,Qare mid-points of DA and BC
⇒ AD=BC [ Sides of square are equal ]
⇒ DP=PA [ P is the mid point ]
⇒ CQ=QB [ Q is the mid point ]
⇒ DA=2AP ---- ( 1 )
⇒ CB=2CQ ---- ( 2 )
From ( 1 ) and ( 2 ),
⇒ 2×AP=2×CQ
⇒ AP=CQ ---- ( 3 )
Now, in △PAB and △QCD
⇒ AP=CQ [ From ( 3 ) ]
⇒ ∠PAB=∠QCD [ Angles of a square is 90o. ]
⇒ AB=CD [ Sides of square ]
⇒ △PAB≅△QCD [ By SAS property ]
⇒ PB=QD [ By CPCT ]
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Answer:
Let, AB=CD=5x according to the parallelogram definition that opposite sides are equal.
AP=3x,PB=2x and CQ=4x, QD=x
⇒ARP∼CRQ
4x
3x
=
RC
AR
RC
AR
=
4
3
According to this fraction, we have
AR=3 & RC=4 so that AC=3+4=7
Finally,
AC
AR
=
7
3
∴AR=
7
3
AC.
Step-by-step explanation:
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