1. A set of 3 whole numbers that satisfy the equation
a2 + b2 = c2
This is the most basic, and
most common Pythagorean
Triple and is often called a
3-4-5 Right Triangle.

2.
625 25
a2 + b2 = c2
= x2
= x2
225 = x2
15 = x

3. 11 25
√11
3.317
3.317

4. a2 + b2 = c2
x = 52
x = 25
x2 = 12.75
x = √12.75
x ≈ 3.571ft
3.5ft
5ft x

5. height
right
225 64 15
120

6. Here's a way to generate the triples:
Let n and m be integers where n>m.
Then, define a = n2 - m2, b = 2nm, c = n2 + m2
Substitution gives:
(n2 - m2)2 + (2nm)2 = (n2 + m2)2
If n = 4 and m = 2, the rule would produce
the Pythagorean Triple 12, 16, 20.

7. 17 3
2601 51

8. a2 + b2 = c2
142 + h2 = 502
196 + h2 = 2500
h2 = 2304
h = 48
A = 1/2bh
A = 1/2(28)(48)
A = 672ft2 h
This is a multiple of the 3, 4, 5 triangle,
so x = 50.