Find the length of the diagonal of the prism.
3 cm wide and 12 cm wide and also 4cm long
To find the length of the diagonal of the prism, we can use the Pythagorean theorem.
The diagonal is the hypotenuse of a right triangle formed by the length, width, and height of the prism.
Let's label the length as a, the width as b, and the height as c.
In this case, a = 3 cm, b = 12 cm, and c = 4 cm.
Using the Pythagorean theorem,
diagonal^2 = a^2 + b^2 + c^2
diagonal^2 = (3 cm)^2 + (12 cm)^2 + (4 cm)^2
diagonal^2 = 9 cm^2 + 144 cm^2 + 16 cm^2
diagonal^2 = 169 cm^2
Taking the square root of both sides, we get:
diagonal = √169 cm^2
diagonal = 13 cm
Therefore, the length of the diagonal of the prism is 13 cm.