2018 · Q71
If base and hypotenuse of a right triangle are (u² - v²) and (u² + v²) respectively and the area of the triangle is 2016 square units, then the perimeter of the triangle may be
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A224 units
- B288 units
- C448 units
- D576 units
Explanation
The other leg is 2uv, so the area is (1/2)(u^2 - v^2)(2uv) = uv(u^2 - v^2) = 2016. Trying u = 9, v = 7: 63 x 32 = 2016, which fits. The perimeter is (u^2 - v^2) + 2uv + (u^2 + v^2) = 2u(u + v) = 2 x 9 x 16 = 288. Hence option B.