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In the adjoining figure, △ABC ~ △QPR.

In the adjoining figure, △ABC ~ △QPR. The value of x is (a) 2.25 cm (b) 4 cm (c) 4.5 cm (d) 5.25 cm. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

The value of x is

  1. 2.25 cm

  2. 4 cm

  3. 4.5 cm

  4. 5.25 cm

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Answer

Since triangles are similar hence the ratio of their corresponding sides are equal.

∴ACQR=BCPR⇒63=4.5x⇒2=4.5x⇒x=4.52⇒x=2.25\therefore \dfrac{AC}{QR} = \dfrac{BC}{PR} \\[1em] \Rightarrow \dfrac{6}{3} = \dfrac{4.5}{x} \\[1em] \Rightarrow 2 = \dfrac{4.5}{x} \\[1em] \Rightarrow x = \dfrac{4.5}{2} \\[1em] \Rightarrow x = 2.25

Hence, Option 1 is the correct option.

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