Mathematics
Grade9
Easy

Question

In the given figure ∆ADE ~ ∆ABC, if AD = 6 cm, DB = 9 cm, and AE = 8 cm, then what will be the value of AC?

  1. 20 cm
  2. 10 cm
  3. 5 cm
  4. 15 cm

hintHint:

If two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion (or) same ratio .

The correct answer is: 20 cm


    Given, ∆ADE ~ ∆ABC.
    In similar triangles ratio of side lengths is same .
    S o comma fraction numerator A D over denominator A B end fraction equals fraction numerator A E over denominator A C end fraction space left parenthesis G i v e n comma space A D space equals space 6 space c m space comma space A B space equals space 15 space c m space a n d space A E space equals space 8 space c m right parenthesis
rightwards double arrow 6 over 15 equals fraction numerator 8 over denominator A C end fraction
rightwards double arrow A C equals space fraction numerator 15 cross times 8 over denominator 6 end fraction equals space fraction numerator 15 space cross times space 4 over denominator 3 end fraction space equals space 5 space cross times space 4 space equals 20 space c m
    Therefore, length of AC = 20 cm.

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