2026 · Q80
In a quadrilateral ABCD, ∠ABC = 90° and ∠ACD = 90°. Let AB = p units, BC = q units, AC = r units, CD = s units, AD = t units, where p < q < r < s < t < 15. If p, q, r, s and t are integers, then what is the area of the quadrilateral?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A24 square units
- B36 square units
- C48 square units
- DCannot be determined due to insufficient data
Explanation
We need Pythagorean triples p² + q² = r² and r² + s² = t² with p < q < r < s < t < 15 integers. The chain 3² + 4² = 5² and 5² + 12² = 13² fits: p = 3, q = 4, r = 5, s = 12, t = 13. The quadrilateral's area is the sum of the two right-triangle areas: ½·3·4 + ½·5·12 = 6 + 30 = 36 square units, option B.