Question

The length of the base of a rectangular prism is 3 feet, and its width of the diagonal of the prism is 6 feet. What is the height of the prism? Express your answer in tenths of a foot.

A. 3.3 ft

B. 13 ft

C. 23 ft

Answer 1

The height of the rectangular prism is found by applying the Pythagorean theorem to its base and diagonal. The calculation shows that the height is approximately 5.2 feet, which is not one of the provided options.

Step-by-step explanation:

To find the height of the rectangular prism, we can use 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 lengths of the other two sides. The diagonal mentioned in the question is the hypotenuse of a right-angled triangle with the length and height of the prism as its other two sides.

Assuming the base is the length, thus:

• The base (length) of the prism: 3 feet
• The diagonal (hypotenuse) of the prism: 6 feet

Let h represent the height of the prism. The Pythagorean theorem gives us:

32 + h2 = 62

Solving for h:

9 + h2 = 36

h2 = 36 - 9

h2 = 27

h = √27

h = 5.2 feet (since √27 is approximately 5.2)

Hence, the height of the prism is approximately 5.2 feet, which is not among the choices provided in the question. Therefore, it could be a typo or the question is missing the right option. Among the given options, none is close to 5.2 feet.