Question

Pythagorean theorem in 3D

What is the length of the diagonal, d, of the rectangular prism shown below?

Answer 1

7

Explanation:

Answer 2

d = 6.997 or 7

Explanation:

Use Pythagorean Theorem to find the diagonal of the end of the prism

2^2 + 3^2 = C^2 Simplify

4 + 9 = C^2 Add

13 = C^2 Take the square root of both sides

3.6 = C

Now plug this into the Pythagorean Theorem equation for the diagonal of the whole prism.

3.6^2 + 6^2 = d^2 Simplify

12.96 + 36 = d^2 Add

48.96 = d^2 Take the square root of both sides

6.997 = d This can be rounded up to 7, if needed