Question

The ratio of the lengths of the respective diagonals of two squares is 2:1.find the ratio of their areas

Answer 1

guess, length of 1st squares = 2x &
length of 2nd squares = x

so, 2x+x=2 : 1
or, 3x=2/1
or,x=2/3

so,lnth of 2nd sqre =2/3 &
     lnth of 1st sqre = 2*2/3 =4/3

ratio of their areas = 4*(4/3)^ : 4*(2/3)^
                              = 4*16/9 : 4*4/9
                              = 64/9 :16/9
                              = 64/9*9/16
                              = 4 :1 [ ∵64/16=4]