Question 93

The areas of two similar triangles ΔABC and ΔPQR are 121 sq cms and 64 sq cms respectively. If PQ = 12 cm, what is the length (in cm) of AB?

Solution

It is given that ΔABC $$\sim$$ ΔPQR

Let length of AB = $$x$$ cm and length of the corresponding side PQ = 12 cm

=> Ratio of Area of ΔABC : Area of ΔPQR = Ratio of square of corresponding sides = $$(AB)^2$$ : $$(PQ)^2$$

=> $$(\frac{x}{12})^2 = \frac{121}{64}$$

=> $$\frac{x}{12}=\sqrt{\frac{121}{64}}=\frac{11}{8}$$

=> $$x=\frac{11}{8}\times12=16.5$$ cm

=> Ans - (C)

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