SOLUTION: help please the diagonal of a square measures 6 inches. what is the length of the sides? the diagonal of a square measures 6 inches. what is the length of the sides? thanks fo

Question 62936: help please
the diagonal of a square measures 6 inches. what is the length of the sides?
the diagonal of a square measures 6 inches. what is the length of the sides?
thanks for your help
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:
The diagonal of a square measures 6 inches. what is the length of the sides?
ANSWER:
For a square all its sides are equal in length and all its four anlges are 90 degree each.
A diagonal of the square divides the square into two right triangles, because it contains one 90 degree.

So we can consider a right trianle whose hypotenuse is 6 inches( diagonal=6 inches)

Let us consider one of the side of this triangle is x inches.

Then other side is = x inches , because both are sides of same square.

so we have, in a right triangle, hypotenuse = 6 inches
base = x inches and
height = x inches

By pythagorus property,

(base)^2 + ( height)^2 = hypotenuse^2

x^2 + x^2 = 6^2

2x^2 = 36

x^2 =36/2

x^2 = 18

Therefore x = square root(18)

= 3sqrt(2)

So lenth of one side of square = 3 sqrt(2)

Regards.
praseenakos@yahoo.co.in

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