Question

Find the diagonal of the rectangular solid

Answer 1

There are four (4) diagonals: 3 face diagonals and one space diagonal. We assume you are interested in the space diagonal.

The face diagonal of the 3×4 face has length
  d₃₄ = √((3 ft)² +(4 ft)²) = √(25 ft²) = 5 ft

Taking the 5 ft edge and the 5 ft face diagonal as sides of the triangle with the space diagonal as its hypotenuse, we find the length of the space diagonal to be
  d = √((5 ft)² +(5 ft)²)
  d = 5√2 ft

The space diagonal of the rectangular solid is 5√2 ft ≈ 7.07 ft.