2012 · Q66
Statement ILet the side DE of a triangle DEF be divided at S so that DS/DE = 1/sqrt(2). If a line through S parallel to EF meets DF at T, then the area of triangle DEF is twice the area of the triangle DST.
Statement IIThe areas of the similar triangles are proportional to the squares on the corresponding sides.
Which one of the following is correct in respect of the above statements?
Elementary MathematicsGeometry
- ABoth statement-I and statement-II are true and statement-II is the correct explanation of statement-I
- BBoth statement-I and statement-II are true but statement-II is not the correct explanation of statement-I
- CStatement-I is true, but statement-II is false
- DStatement-II is true, but statement-I is false
Explanation
Triangles DST and DEF are similar with linear ratio 1/sqrt(2), so the area ratio is 1/2; statement-II is the similarity area theorem that explains this.