Answer:
19.8
Step-by-step explanation:
To find out the length of the diagonal of a square, first we need the length of it sides. We will get this information from the perimeter.
We calculate the perimeter of a square adding up the length of the 4 sides. As all the sides of a square are equal, we just take one side and multiply it by four.
So, if the perimeter is 56 cm, that means 56 = 4*L, where L represents the length of the sides. If we want to know the value of L, we have to divide by 4 on both sides:
56 = 4*L
56/4 = 4/4*L
14 = L
Now we can find out the length of the diagonal using the Pythagorean equation
[tex]\fbox {\textbf{Pythagorean equation}:}[/tex] The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle)
In this case, the hypotenuse is the diagonal we want to find out and the legs are the two sides of the square.
So, we have
[tex]D^2 = L^2 + L^2[/tex]
[tex]D^2 = 14^2 + 14^2[/tex]
[tex]D^2[/tex] = 392
[tex]D = \sqrt{392}[/tex]
D = 19.8
