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 th
e diagonal?
The equation that would help you with the first step of finding the length of the diagonal of the rectangular prism is the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the diagonal length forms the hypotenuse of a right-angled triangle, with the length and width of the rectangular prism forming the other two sides.
The equation representing the Pythagorean theorem in this context would be:
diagonal length^2 = length^2 + width^2
Let's substitute in the given values for the length and width:
diagonal length^2 = 9^2 + 6^2
diagonal length^2 = 81 + 36
diagonal length^2 = 117
Therefore, the first step in finding the length of the diagonal of the rectangular prism would be to find the square root of 117.