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 solve step by step

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Answer 1

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 ]

HOPE IT WILL HELP YOU....

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:

Thank you sooooo much sista