Question

Mckenzie and Cara both tried to find the missing side of the right triangle.

Mckenzie's Work Cara's Work
a2 + b2 = c2 a2 + b2 = c2
52 + 132 = c2 52 + b2 = 132
25 + 169 = c2 25 + b2 = 169
194 = c2 b2 = 144
Square root 194 equals square root c squared. Square root b squared equals square root 144.
13.93 ≈ c b ≈ 12
Is either of them correct? Explain your reasoning.

Answer 1

Answer: Mckenzie is correct

I had to reformat this section with the way it was typed, please let me know if I did anything wrong.

Mckenzie's Work

a² + b² = c²

25 + 169 = c²

194 = c²

Square root 194 equals square root c squared.

c ≈ 13.93

Cara's Work

a² + b² = c²

25 + b² = 169

b² = 144

Square root b squared equals square root 144.

b ≈ 12

[] Right away we can tell that Cara is not correct.

-> Cara solves for b. We already have a b value, we need to solve for "c" in the equation.

[] Now let's look at Mckenzie.

-> Mckenzie does solve for the right variable, so let's see if she did it correctly.

-> First, she sets is up using a² + b² = c² since this is a right triangle. Next, she squares 5 to 25 and 13 to 169. Both correct.

-> Now they are added together. 25 + 169 do equal 194 so this looks correct.

-> Last, we square both sides.
`√(194)` ≈ 13.928388 which rounds to 13.93, so it looks like Mckenzie is correct.

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather