2026 · Q51
The perimeter of a right-angled isosceles triangle is 20 units. If α is the area of the triangle, then
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A15 < α < 16
- B16 < α < 17
- C17 < α < 18
- D18 < α < 19
Explanation
With legs ℓ, the perimeter ℓ(2+√2)=20 gives ℓ=10(2−√2). The area ℓ²/2=300−200√2≈17.16, which lies between 17 and 18, option C. Numerically ℓ≈5.857, so the area ℓ²/2≈17.16, comfortably inside the 17–18 band.