CDS 2026 (I) Elementary Mathematics, question 49

Topic: Geometry

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Q49

ABC is a triangle right-angled at B with sides BC=aBC=a, CA=bCA=b and AB=cAB=c. Let pp be the length of the perpendicular from B to AC. Which of the following statements is/are correct ?

I. p=aca2+c2p=\frac{ac}{\sqrt{a^{2}+c^{2}}}

II. pb=acpb=ac

Select the answer using the code given below :

  1. (a) I only
  2. (b) II only
  3. (c) Both I and IICorrect answer
  4. (d) Neither I nor II

Solution.

Answer: (c) Both I and II

  1. Compute the triangle's area using its perpendicular legs and then its hypotenuse: ac/2=bp/2ac/2 = bp/2, so bp=acbp = ac.
  2. Since b=a2+c2,p=ac/a2+c2b = \sqrt{a^{2} + c^{2}},p = ac/\sqrt{a^{2} + c^{2}}.
  3. Both statements follow from the same area identity.