Question 98

ΔPQR is right angled at Q. QS is the altitude. PQ is 4√13 cm and PS is 8 cm. What is the length of SR?

Solution

Given : PQ = $$4\sqrt{13}$$ cm and PS = 8 cm

In $$\triangle$$ PQS, => $$(PQ)^2=(PS)^2+(QS)^2$$

=> $$(4\sqrt{13})^2=(8)^2+(QS)^2$$

=> $$(QS)^2 = 208-64 = 144$$

=> $$(QS)=\sqrt{144}=12$$ cm

Let SR = $$x$$ cm

Using, $$(QS)^2 = (PS) \times (SR)$$

=> $$(12)^2 = 8 \times x$$

=> $$x = \frac{144}{8} = 18$$ cm

=> Ans - (C)

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