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.
