1. Question 34

2. Question 34
Triangle STV has sides with lengths of 7, 11, and 14 units. Determine whether this triangle is a right triangle. Show all work necessary to justify your answer.
This is not a right triangle because the two sides of the equation do not equal each other.
a2 + b2 = c2
= 142
The students can use calculators for this problem. It’s also worth 2 points—1 point for each part.
This problem is using Pythagorean Theorem. For it, you need to see if when you square and add the two smaller sides, if they equal the square of the larger side. If they do, then it is a right triangle. If they don’t, then it’s not a right triangle.
You start with the Pythagorean Theorem: a2 + b2 = c2
Then you plug in the values that are you given. 7 and 11 go in for a and b. 14 goes in for c.
When you square the sides you get 49 and When you square the hypotenuse, you get 196.
When you add the left side, you get that 170 is equal to 196.
Since that statement is FALSE, this is not a right triangle.
= 196
170 = 196

3. Question 34
A right triangle has a hypotenuse with a length of 15. The lengths of the legs are whole numbers. What are the lengths of the legs?
9 and 12
a2 + b2 = c2
= 152
For this problem, there are many ways the students could solve it. Without knowing it off the top of their head, they might want to guess and check to see. In order to that, you know that 15 needs to be the largest number you are using. No number over 15 will be used. As it turns out, it ends up being 9 and 12. The students probably just guessed, if they did not know this already. The rest of the slide is a proof to show that it works.
= 225
225 = 225