question_answer

The ratio of area of a square to another a square drawn on its diagonal is

A)  3 : 4                

B)  4 : 5

C)  2 : 3                

D)  1 : 2

Correct Answer: D

Solution :

[d] Let ABCD is a square whose side is ?a? units. DB is its diagonal and DBQP is square drawn in diagonal DB of square ABCD Area of ABCD \[=a\times a={{a}^{2}}\]                       ? (1) From \[\Delta ABD\] \[D{{B}^{2}}=A{{B}^{2}}+A{{D}^{2}}\] \[D{{B}^{2}}={{a}^{2}}+{{a}^{2}}\] \[\Rightarrow \] \[DB=a\sqrt{2}\] Area of square \[DBQP=a\sqrt{2}\times a\sqrt{2}=2{{a}^{2}}\]  ? (2) From (1) and (2) Area of square: Area of square \[DBQP={{a}^{2}}:2{{a}^{2}}=1:2\]