Question

which of the following are pythagorean triples? select all that apply.
show your work here
(12, 16, 20)
(8, 15, 17)
(3, 4, 5)
(9, 12, 15)
(4, 7, 9)

Explanation:

Step1: Test (12,16,20)

Check $12^2 + 16^2 = 20^2$

$$\begin{aligned} 12^2 + 16^2 &= 144 + 256 = 400 \\ 20^2 &= 400 \end{aligned}$$

Step2: Test (8,15,17)

Check $8^2 + 15^2 = 17^2$

$$\begin{aligned} 8^2 + 15^2 &= 64 + 225 = 289 \\ 17^2 &= 289 \end{aligned}$$

Step3: Test (3,4,5)

Check $3^2 + 4^2 = 5^2$

$$\begin{aligned} 3^2 + 4^2 &= 9 + 16 = 25 \\ 5^2 &= 25 \end{aligned}$$

Step4: Test (9,12,15)

Check $9^2 + 12^2 = 15^2$

$$\begin{aligned} 9^2 + 12^2 &= 81 + 144 = 225 \\ 15^2 &= 225 \end{aligned}$$

Step5: Test (4,7,9)

Check $4^2 + 7^2 = 9^2$

$$\begin{aligned} 4^2 + 7^2 &= 16 + 49 = 65 \\ 9^2 &= 81 \end{aligned}$$

Answer:

(12, 16, 20), (8, 15, 17), (3, 4, 5), (9, 12, 15)