Find the length of the diagonal of the prism.
the length is 4 cm, the height is 12 cm, and the width is 3 cm.
The diagonal of the prism can be found using the Pythagorean Theorem.
Let's denote the length, height, and width of the prism as L, H, and W respectively.
By applying the Pythagorean Theorem to the base of the prism, we have:
diagonal of the base = √(L^2 + W^2)
= √(4^2 + 3^2)
= √(16 + 9)
= √25
= 5 cm
Now, we need to find the diagonal of the prism, which is a right triangle with sides 5 cm and 12 cm.
Using the Pythagorean Theorem again, we have:
diagonal of the prism = √(5^2 + 12^2)
= √(25 + 144)
= √169
= 13 cm
Therefore, the length of the diagonal of the prism is 13 cm.