Question

What is the length of the diagonal of a square of the square has a perimeter of 60 inches

Answer 1

15 sqrt(2)

Explanation:

The perimeter of a square is given by

P = 4s where s is the side length

60 = 4s

Divide each side by 4

60/4 = 4s/4

15 =s

The diagonal is the hypotenuse of the right triangle where the legs are the sides of length 15

Using the Pythagorean theorem

a^2 + b^2 = c^2

15^2 + 15^2 = c^2

225+225 = c^2

450 = c^2

Taking the square root of each side

sqrt(450) = sqrt( c^2)

sqrt (2*225) = c

We know that sqrt(ab) = sqrt(a) sqrt(b)

sqrt(2) sqrt(225) =c

sqrt(2) 15 = c