Find the length of the diagonal of the prism. 12, 3, 4
To find the length of the diagonal of a prism, we can use the Pythagorean theorem.
Let the sides of the base of the prism be a = 12 and b = 4, and the height of the prism be c = 3.
The diagonal of the base can be found using the Pythagorean theorem:
d1 = sqrt(a^2 + b^2)
= sqrt(12^2 + 4^2)
= sqrt(144 + 16)
= sqrt(160)
= 12.65
The diagonal of one of the rectangular faces of the prism is equal to this value, d1 = 12.65.
The diagonal of the prism can be found by using the Pythagorean theorem again, now considering the height of the prism.
d2 = sqrt(d1^2 + c^2)
= sqrt(12.65^2 + 3^2)
= sqrt(160.0225 + 9)
= sqrt(169.0225)
= 13
Therefore, the length of the diagonal of the prism is 13.