Mathematics
Grade9
Easy

Question

Find the length of CD of the following figure if AB ll  DE.

  1. 2.5 cm
  2. 2.7 cm
  3. 3 cm
  4. 2.25 cm

hintHint:

Prove the similarity of triangles and if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion then find the value of 

The correct answer is: 2.7 cm


    Given, AB ll DE,
    alternate angles are equal so, angle B equals space angle D, and
     angle B C A equals space angle E C D( vertically opposite angles are equal)
    By AA similarity, ΔCAB ~  ΔCED
    corresponding sides are in equal proportion for similar triangles.
    fraction numerator E D over denominator A B end fraction space equals space fraction numerator C D over denominator C B end fraction space left parenthesis G i v e n space E D space equals space 3 space c m space comma A B space equals space 5 space c m space a n d space C B space equals space 4.5 space c m space F r o m space d i a g r a m right parenthesis
3 over 5 equals fraction numerator C D over denominator 4.5 end fraction
C D equals fraction numerator 4.5 cross times 3 over denominator 5 end fraction equals space 0.9 space cross times space 3 space equals space 2.7 space c m
    Therefore, Side length of CD is 2.7 cm.

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