2026 · Q55
ABC is a triangle right-angled at C. Let P be the midpoint of BC. If AP = 4√13 cm and AB = 20 cm, then what is the perimeter of the triangle ABC?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A40 cm
- B48 cm
- C50 cm
- D60 cm
Explanation
Put AC=x and BC=2y (P is the midpoint): AP²=x²+y²=208 and AB²=x²+4y²=400. Subtracting gives 3y²=192, so y=8 and x=12; the sides are 12, 16, 20 and the perimeter is 48 cm, option B. The sides 12-16-20 are just the 3-4-5 triangle scaled by 4, a useful sanity check.