2018 · Q83
The areas of two similar triangles are (7-4{3})\,{cm}² and (7+4{3})\,{cm}² respectively. The ratio of their corresponding sides is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A7 - 434√{3}
- B7 - 333√{3}
- C5 - 3√{3}
- D5 + 3√{3}
Explanation
The ratio of corresponding sides is the square root of the area ratio: sqrt((7 - 4 sqrt(3))/(7 + 4 sqrt(3))). Since (7 - 4 sqrt(3))/(7 + 4 sqrt(3)) = (7 - 4 sqrt(3))^2 (multiplying top and bottom by 7 - 4 sqrt(3), denominator 49 - 48 = 1), the ratio is 7 - 4 sqrt(3). Hence option A.