Need Some Help please. (1 Viewer)

[Earache]

A 5 x 5 grid has 16 squares on the border. How many squares will be on the border of a 10 x 10 grid ?

I need 2 different solutions and how they are related?

 

[bored of sc]

64 and 81.

64 from ratio of side of square to square root of number of squares on the border.
>5:4 = 10:x
4/5 = x/10
x = 8
> Then square 8
= 64

81 if you take each as a perfect square;
> Square root of squares on border is one less than side of square grid
5² for grid
(5-1)² = 4² = 16 for number of squares on border.
> Therefore for unknown value 10² for grid
(10-1)² = 9² = 81 squares on border.

Maybe.

Both answers are related since you are squaring your values of 8 and 9 in each case.

What topic is this by the way?

EDIT: 32 may work as well.

Since you double side of square from 5 to 10, double the number of squares on border. 16 x 2 = 32.

Am I making any sense at all?

 

[lolokay]

10 across top and bottom, 8 across the sides. Total = 36 (in general, for a square board of sides n it will be 4(n-1), for a rectangle with sides m and n it will be 2(n-1) + 2(m-1) -> for m and n >1)

not sure what '2 different solutions means though'. How can there be more than 1?