Each side of a square is 15in long. Find the length of the diagonal to the nearest tenth

Question

Each side of a square is 15in long. Find the length of the diagonal to the nearest tenth

Answer 1

Diagonal of the square is the hypotenuse of the right isoscele triangle, which is equal to √2 times leg: 15√2.

Answer 2

the diagonal forms two isosceles right triangles  (45-45-90 triangles)

using one of them and the Pythagorean Theorem...

15^2+15^2=d^2

225+225=d^2

450=d^2

d^2=450

take the square root of both sides

d=√450

d=√(225)(2)

d=15√2 inches

in a 45-45-90 right triangle the hypotenuse (in this case the diagonal)  is always x√2 where x=side length

you really don't have to use the Pythagorean Theorem, just use x√2 where x=15

d=15*1.414

d=21.21

d=21.2 inches