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Rajan@2021
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In the figure given below, ABparallelDC.AO=10 cm,OC=5 cm,AB=6.5 cm and OD=2.8 cm. (i) Prove that △OAB∼△OCD. (ii) Find CD and OB (iii) Find the ratio of areas of △OAB and △OCD

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In the given figure we have been  given the length of sides AO=10 cm,OC=5 cm,AB=6.5 cm and OD=2.8 cm and we are to

(i) Prove that △OAB∼△OCD.

(ii) Find CD and OB

(iii) Calculate the ratio of areas of △OAB and △OCD

ML Aggarwal, Avichal Publication, class 10, Similarity, chapter 13.3, question no 5b

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1 Answer

  1. From the question it is given that,
    ABDC.AO=10cm,OC=5cm,AB=6.5cm and OD=2.8cm
    (i) We have to prove that, OABOCD
    So, consider the OAB and OCD
    AOB=COD … [because vertically opposite angles are equal]
    OBA=OCD … [because alternate angles are equal]
    Therefore, OABOCD … [from AAA axiom]
    (ii) Consider the OAB and OCD
    OA/OC=OB/OD=AB/CD
    Now consider OA/OC=OB/OD
    10/5=OB/2.8
    OB=(10×2.8)/5
    OB=2×2.8
    OB=5.6cm
    Then, consider OA/OC=AB/CD
    10/5=6.5/CD
    CD=(6.5×5)/10
    CD=32.5/10
    CD=3.25cm
    (iii) We have to find the ratio of areas of OAB and OCD.
    From (i) we proved that, OABOCD
    Then, area of (OAB)/area of OCD
    AB2/CD2=(6.5)2/(3.25)2
    =(6.5×6.5)/(3.25×3.25)
    =2×2/1
    =4/1
    Therefore, the ratio of areas of OAB and OCD=4:1.

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