Pythagorean Theorem(geometry) question?

Question

The diagonals of a square bisect each other at right angles. if each diagonal is 14 hectometres long, how long is each side of this square?
How would I figure this out?
There is an answer I have found, but want to see if I am right

Answer 1

Well, each diagonal forms an isosceles right triangle.

So we can use a² + b² = c²... but since it's a square.. a = b

So..

a² + a² = c²
2a² = c²

a² = c²/2

a² = (14)²/2
a = sqrt(14²/2)
a = 14 / sqrt 2 = 14 sqrt 2 / 2 = 7 sqrt(2) hm

a is about 9.9 hm

Answer 2

1 of the diagonals makes a right angle triangle with 2 equal sides.

The square on the hypotenuse = the sum of the squares of the other two sides. Let's call the two sides 'A'.

14² = 2A²
196 = 2A²

A = √196/2 = √98 = 9.9 hectometres each side.

Answer 3

YOu first divide 14 hectometers in half ( to get the length of one half of the diagonal) Then it forms a Right triangle, right? Cause the diagonals bisect, so they are each 90 degree angles.

Next, you do A squared + B squared = C squared, 7 squared + 7 squared = C squared and solve from there. Sorrry, dont have a calculator, and dont feel like doin it in my head. LoL

Answer 4

Consider only one of the diagonals. It divides the square into two triangles, of sides x, x, and 14. You can show by Pythagoras that if the side of such a triangle is 1, the hypotenuse is sqrt(2). Therefore, x = 14/sqrt(2), or 7 sqrt(2), or about 10.

Answer 5

a square plus b square equals c square.
a2+b2=c2
multiply the number by itself, and then to the same to the other one...add it and then divide it...i give up...i'm confused!!

Answer 6

2l^2=14^2=>l^2=14^2/2
l= sqrt(14^2/2)=>
l=14/sqrt2=>l=7sqrt(2)

Answer 7

9.899 hectometers

Answer 8

9.899hectometers?