Answer:
10√2 inches (second option)
Step-by-step explanation:
visualise a square in your head. then, imagine a diagonal running through it. that diagonal would separate the square into two triangles. so to find the diagonal, we first need to find the length of the square (which would serve as the base and height of the triangle).
we can simply divide the perimeter by 4 to get the length of each side, which would then be 40 ÷ 4 = 10.
next, we can use the formula of the pythagorus theorum! it states that a² + b² = c², where a, b and c are represented by the following image:
for our equation, this would translate to 10² + 10² = c², and c would be the length of the diagonal.
100 + 100 = c²
200 = c²
in radical form, the square root of 200 would be 10√2. therefore, the length of the diagonal is 10√2 inches, which is the second option.
i hope this helps! :D