CDS 2026 (I) Elementary Mathematics, question 51

Topic: Mensuration

Answers by SolvedPaper. UPSC has not released the official answer key for this paper yet. We will update it when they do.

Q51

The perimeter of a right-angled isosceles triangle is 2020 units. If α\alpha is the area of the triangle, then

  1. (a) 15<α<1615<\alpha<16
  2. (b) 16<α<1716<\alpha<17
  3. (c) 17<α<1817<\alpha<18Correct answer
  4. (d) 18<α<1918<\alpha<19

Solution.

Answer: (c) 17<α<1817<\alpha<18

  1. Let each equal leg be a.
  2. The perimeter condition gives a(2+2)=20a\left( 2 + \sqrt{2} \right) = 20, so a=10(2−2)a = 10\left( 2 - \sqrt{2} \right).
  3. The area is α=a2/2=300−2002\alpha = a^{2}/2 = 300 - 200\sqrt{2} ≈ 17.157.