find the length of the diagonal of the prism. 12 cm, 3 cm, and 4 cm
To find the length of the diagonal of a prism, we need to use the Pythagorean theorem. The diagonal is the hypotenuse of a right-angled triangle formed by two sides of the prism.
Let's call the height of the prism, which corresponds to the shorter side, h. The length of the base is 12 cm, and the width is 4 cm.
Using the Pythagorean theorem, we can write:
h^2 + 4^2 = 12^2
Simplifying, we have:
h^2 + 16 = 144
Subtracting 16 from both sides, we get:
h^2 = 128
To find the length of the diagonal, we need to find the diagonal of the base and the height. Using the Pythagorean theorem again, we have:
Diagonal of base = √(12^2 + 4^2)
= √(144 + 16)
= √160
= 12.65 cm
Diagonal of height = √(12.65^2 + h^2)
= √(160 + 128)
= √288
= 16.97 cm
Therefore, the length of the diagonal of the prism is approximately 16.97 cm.