Question

The rectangular prism below has a length of 9 ft., a width of 6 ft., and a height of 3 ft. You want to find the diagonal length from the bottom corner of the prism to the top corner. Which equation would help you with the first step of finding the length of the base of the prism.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The equation that would help you with the first step of finding the length of the base of the prism is the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

In this case, you can use the Pythagorean theorem to find the length of the base of the prism (the bottom of the rectangular face) by considering it as the base of a right triangle where the two legs are the width and height of the prism.

So the equation would be:

base^2 + height^2 = diagonal^2

Using the given values:

6^2 + 3^2 = diagonal^2

36 + 9 = diagonal^2

45 = diagonal^2

Now you can take the square root of 45 to find the diagonal length from the bottom corner of the prism to the top corner.