Question

the diagonal of a square is 11cm. What is the perimeter of the square ?

Answer 1

do you know the formula to calculate the perimeter of square

its 4 * (length of side)

Answer 2

you have a square with diagonal 11
use law of sines to get the length of the side
sin(45)/x = sin(90)/11
x/11 = sqrt(2)/2
x = 11sqrt(2)/2
perimeter is 4x
so
4*11sqrt(2)/2 = 22sqrt(2)

Answer 3

does that make sense @1LiveToBreath

Answer 4

@zzr0ck3r You could use the 45-45-90 theorem in reverse.

The diagonal of a square is the hypotenuse of a 45-45-90 triangle.
So, the diagonal is square root of 2 times a side of the 45-45-90 triangle or the square in this case.

One side of the square would be 11/sqrt(2) and then multiply that by 4.
That is essentially what you did but this route may be a little faster.

Remember this, too: The diagonal of a cube is sqrt(3) times one of its edges. That comes in handy.

Answer 5

\[\sqrt{2}a=11\] where a is the side of square!

Answer 6

\[a=\frac{ 11 }{ \sqrt{2} }\]\[perimeter=4*\frac{ 11 }{ \sqrt{2} }=\frac{ 44 }{ \sqrt{2} }=22\sqrt{2}\]