Question

Lucy says the hypotenuse is 15 Annie says its 117. Timo says it rounds to 11.

Explain who is right. PROVE your answer using Pythagoras visually or numerically.

Answer 1

Answer: Timo is correct; the hypotenuse rounds to 11

Work Shown:

`a^2+b^2 = c^2\\\\c = √(a^2+b^2)\\\\c = √(6^2+9^2)\\\\c = √(36+81)\\\\c = √(117)\\\\c \approx 10.81665\\\\c \approx 11\\\\`

This confirms Timo is correct.

It appears Lucy mistakenly added the side lengths 6 and 9 to get 6+9 = 15, which is not the correct way to get the hypotenuse.

Annie mentioning the 117 seems to suggest that she might have forgotten about the square root, since we got
`√(117)` earlier in the steps shown above.

If Annie said
`\text{The hypotenuse is } √(117) \text{ units long}`, then she would be correct. Though it's probably better to go with the decimal form (rounding however you want) to get a better sense of how long the hypotenuse is.