find the length of the diagonal of the prism.
12cm tall, 3cm wide, 4cm long
To find the length of the diagonal of the prism, we can use the Pythagorean theorem.
Let's label the dimensions of the prism as follows:
Height (h) = 12 cm
Width (w) = 3 cm
Length (l) = 4 cm
Now, we can calculate the length of the diagonal (d) of the prism using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
The diagonal d can be represented by the hypotenuse, while the other two sides (a and b) can be represented by the width and length respectively.
Applying the Pythagorean theorem, we have:
d² = w² + l²
d² = 3² + 4²
d² = 9 + 16
d² = 25
Taking the square root of both sides, we find:
d = √25
d = 5 cm
Therefore, the length of the diagonal of the prism is 5 cm.