The areas of three fields are 165 sq.m , 195 sq .m and 285 sq.m respectively. From these, flower beds of equal sizes are to be made. If the breadth of each bed is 3m, what will be the maximum length of each bed

Answer :

Given  : The areas of three fields are 165 m² , 195 m² and 285 m² .
And
 If the breadth of each bed is 3 m,
So,
To find the  maximum length of each bed , We find Highest possible area of bed of equal sizes that can be made in three fields , So

We find HCF of 165  , 195 and 285 

165  = 3 $\times$  5 $\times$ 11
And
195  =  3 $\times$ 5 $\times$ 13
And
285  =  3 $\times$ 5  $\times$ 19

So,

HCF ( 165 ,  195  and 285 ) =  3 $\times$ 5   =  15

So,

Maximum area of flower bed  =  15 m²

So,

Maximum length  if breadth is 3 m  =  $\frac{15}{3}$ = 5 m                                   ( Ans )