Question

Patrice says that she can find the length of the diagonal, c, of the rectangular prism by using the Pythagorean theorem twice.

Drag equations and pictures into the table below to show her work.

Answer 1

see attached

Explanation:

The first application of the Pythagorean theorem is used to find the diagonal of one face. That is called 'a' in this problem. Then the second application of the Pythagorean theorem uses that value of 'a' along with the remaining prism dimension to find the space diagonal 'c'.

• 6² +8² = a²
• 12² +a² = c²

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You don't actually have to find 'a', because you only need the value of a². Using the first equation to substitute into the second equation gives ...

6² +8² +12² = c²