Mr. Pythagoras wouldn't let this triangle into his Pythagorean Triple Club even if it begged.
Answer
Example 2
Find the value of x.
Hint
In this triangle, x is the shortest leg.
Answer
Example 3
Find the value of x.
Hint
Both the legs of the triangle are the same length. That means that in terms of the Pythagorean Theorem, x = a = b.
Answer
x = √18 ≈ 4.2
Example 4
A triangle has side lengths of , , and . Is the triangle a right triangle?
Hint
What's the Converse Pythagorean Theorem again?
Answer
No, it is not a right triangle.
Example 5
Determine whether ∆XYZ is a right triangle and/or a Pythagorean triple if its vertices are at the points X (1, 1), Y (1, 7), and Z (9, 1).
Hint
A Pythagorean triple will always make a right triangle.
Answer
The triangle is both a right triangle and a Pythagorean triple.
Example 6
If the distance between A and B is 26, what is the value of y?
Hint
Drawing a line from B down to the x-axis at a right angle might help.
Answer
y = 10
Example 7
Find the value of x.
Hint
The Pythagorean Theorem can give us the hypotenuse of the largest triangle. Then, we can use the geometric mean to find a. Once we know a, we can figure out what x is.
, 
, and 
. Is the triangle a right triangle?
