Question

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.

Please tell fast​

Answer 1

Answer:

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We know that ABCD is a square and P,Q are 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 90

o

. ]

⇒ AB=CD [ Sides of square ]

⇒ △PAB≅△QCD [ By SAS property ]

⇒ PB=QD [ By CPCT ]

Answer 2

Answer:

We know that ABCD is a square and P,Q are 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 90

o

. ]

⇒ AB=CD [ Sides of square ]

⇒ △PAB≅△QCD [ By SAS property ]

⇒ PB=QD [ By CPCT ]

Step-by-step explanation:

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