Question

The areas of three rectangular field are 165m²,195m²and 285m²​​. The three fields are divided into some smaller rectangular parts of equal areas. If the breath of each part is 3m, then find the length of the each part.

Answer 1

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 × 5 × 11
And
195 = 3 × 5 × 13
And
285 = 3 × 5 × 19

So,

HCF ( 165 , 195 and 285 ) = 3 × 5 = 15

So,

Maximum area of flower bed = 15 m2

So,

Maximum length if breadth is 3 m = 15/3 = 5 m ( Ans )