Answer: 12.73 inches
Step-by-step explanation:
In order to find the length of a squares diagonal given its perimeter, we must find the value of each side length, and then use the pythagorean theorem to get the diagonal.
Solving:
Since there are 4 equal sides in a square, we can write the perimeter as:
[tex]\[ 4s = 36 \][/tex]
Where [tex]s[/tex] represents a side.
To get the individual side length, we just divide by 4:
[tex]\\\frac{4s}{4} = \frac{36}{4} \\\\{\[ s = 9 ~\]}[/tex]
Now plug into the pythagorean theorem:
[tex]\boxed{~d^2= a^2 + b^2}\\ \\\text{In this equation:} \\\quad d \text{ represents the length of the diagonal.} \\\quad a \text{ and } b \text{ represent the lengths of the other two sides of the right triangle.}[/tex]
Now plug in 9 for [tex]a[/tex] and [tex]b[/tex]:
[tex]\[ d^2 = s^2 + s^2 \]\\ d^2 = 9^2 + 9^2 \]\\d^2 = 81 + 81 \]\\\\\boxed{d^2 = 162~ }[/tex]
Now square root both sides to get the diagonal:
[tex]d = \sqrt{162} \\\boxed{d \approx 12.73 \text{ inches} }[/tex]
Therefore, the diagonal is 12.73 inches.
