Question

the area of a square is numerically less than six times its side list some squares in which this happens​

Answer 1

Answer:

All having the side of length ( 1 , 2 , 3 , 4 or 5 ) will be listed in this.

Step-by-step explanation:

Let the length of that square be a. { a € N }

From the properties of square, we know : area if any square is equal to the square( side to the power 2 ) of its side.

According to the question :

= > area > six times of its side

= > a^2 > 6a

= > a^2 - 6a > 0

= > a( a - 6 ) > 0

= > a > 0 or a - 6 > 0

= > a > 0 or a > 6

Numeric value of a can't be 0 since it is length a square. Therefore, a > 6.

Solution set is { 1 , 2 , 3 , 4 , 5 }

Hence it can be stated that all having the side of length ( 1 , 2 , 3 , 4 or 5 ) will be listed in this.

Answer 2

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

Let the side of the square be x.

According to the question, we can write,

$\leadsto \tt {{x}^{2}<6x}$

$\leadsto \tt {{x}^{2}-6x <0}$

$\leadsto \tt {x (x-6)<0}$

So, there are two possibilities :-

$\leadsto \tt {x <0\:OR\:x-6 <0}$

$\leadsto \tt {x <0\:OR\:x <6}$

Now, side of a square can not be less than 0.

So, the answer is :- $\huge\tt {\boxed {x <6}}$

So, the list of the side of the square in which this is possible is :-$\huge\tt {\boxed {1,2,3,4\:and\:5.}}$

$\rule {200}2$