Question

There’s a 3-dimensional rectangle with a 3 underneath and a 12 and 4 on each side

Find the length of the diagonal of the prism

Answer 1

To find the length of the diagonal of the prism, we can use the Pythagorean theorem.

Let's call the length of the rectangle L, the width W, and the height H. According to the information given, we have:

L = 12
W = 4
H = 3

To find the diagonal, we need to find the diagonal of the rectangle formed by the sides of the prism (which has length L and width W) and the height H.

Using the Pythagorean theorem, the length of the diagonal (D) can be calculated as:

D = √(L^2 + W^2 + H^2)

Substituting the values we have:

D = √(12^2 + 4^2 + 3^2)
D = √(144 + 16 + 9)
D = √169
D = 13

Therefore, the length of the diagonal of the prism is 13 units.