Question

The length of the hypotenuse of a right triangle is 145 units. The length of one leg of the triangle is 144. Mike wrote the following step to find the length of the unknown leg:
Length of the unknown leg = 1452 - 1442 = 21,025 - 20,736 = 289 units
Which statement best explains whether Mike's step is correct or incorrect?

Answer 1

I guess a lot of formatting is missing on your question, so these are the correct steps: using the inverse Pythagorean theorem, we know that the length of the missing side is the square root of the difference of the squares of the hypotenuse and the other leg.

Let x be the length you're looking for, we have

$x = \sqrt{145^2-144^2}=\sqrt{21025-20736}=\sqrt{21025-20736}=\sqrt{289}=17$

So, it looks like Mike's missing the last step: what he found is the square of the missing leg's length, not its actual length.