2024 · Q13
ABC is a right-angled triangle, right-angled at B such that AB = 6 cm and BC = 8 cm. What is the perimeter of the square inscribed in the triangle ABC with maximum area?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A24/7 cm
- B96/7 cm
- C24 cm
- D32 cm
Explanation
Let the inscribed square have side s with one corner at B. By similar triangles, s/6 + s/8 = 1, giving s = 24/7 cm. Its perimeter is 4s = 96/7 cm, option (b).