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Rajan@2021
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In the given figure, AB and DE are perpendicular to BC. (i) Prove that ΔABC ~ ΔDEC (ii) If AB = 6 cm DE = 4 cm and AC = 15 cm. Calculate CD. (iii) Find the ratio of the area of ΔABC : are a of ΔDEC

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In the given figure, AB and DE are perpendicular to BC.

(i) Prove that ΔABC ~ ΔDEC

(ii) If AB = 6 cm DE = 4 cm  and AC = 15 cm. Calculate CD.

(iii) Find the ratio of the area of ΔABC : are a of ΔDEC

ML Aggarwal Avichal Publication class 10, similarity chapter 13.3, question no 8

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1 Answer

  1. (i) From ΔABC and ΔDEC,
    ABC=DEC=90 (Given)
    and ACB=DCE= Common
     ΔABCΔDEC (By AA similarity)
    (ii) In ΔABC and ΔDEC,
    ΔABCΔDEC       (proved in (i) part)
    ∴AB/DE=AC/CD
    Given: AB=6 cm,DE=4 cm,AC=15 cm,
    ∴6/4=15/CD
    6×CD=15×4
    CD=60/6
    CD=10 cm.
    (iii) Area of ΔDECArea of ΔABC=AB2​/DE2        (ΔABCΔDEC)
    =(4)2(6)2=36/16=9/4
     Area of ΔABC: Area of ΔDEC=9:4

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