2016 · Q59
ABC and DEF are similar triangles. If the ratio of side AB to side DE is (√(2)+1) : √(3) then the ratio of area of triangle ABC to that of triangle DEF is
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A(3-2√(2)) : 3
- B(9-6√(2)) : 2
- C1 : (9-6√(2))
- D(3+2√(2)) : 2
Explanation
The area ratio is the square of the side ratio: ((√2+1)/√3)² = (3+2√2)/3. Rationalising gives 1/(9−6√2) = (9+6√2)/9 = (3+2√2)/3. The two forms match, so the ratio is 1:(9−6√2), option C.