The perimeter of a right-angled isosceles triangle is 20 units. If \alpha is the area of the triangle, then

  1. A. 15 < \alpha < 16
  2. B. 16 < \alpha < 17
  3. C. 17 < \alpha < 18 ✓
  4. D. 18 < \alpha < 19

Correct Answer: C. 17 < \alpha < 18

Explanation

Let the equal sides be a. The hypotenuse is a\sqrt{2}. Perimeter = 2a + a\sqrt{2} = 20, so a = \frac{20}{2+\sqrt{2}} = 10(2-\sqrt{2}). Area \alpha = \frac{1}{2}a^2 = 50(2-\sqrt{2})^2 = 50(6-4\sqrt{2}). Using \sqrt{2} \approx 1.414, \alpha \approx 50(6 - 5.656) = 17.2, so 17 < \alpha < 18.

Related questions on Mensuration

Practice more CDS Elementary Mathematics questions