Question

unit 7 test sp 26
which of the choices below represents a pythagorean triple?
○ 6, 10, $5\sqrt{3}$
○ 48, 55, 73
○ 8, 8, $\sqrt{32}$
● 20, 21, 30

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle with sides $a \leq b < c$, the theorem states $a^2 + b^2 = c^2$.

Step2: Test Option 1: $6, 10, 5\sqrt{3}$

Calculate $6^2 + (5\sqrt{3})^2 = 36 + 75 = 111$, and $10^2 = 100$. $111
eq 100$, so not a triple.

Step3: Test Option 2: $48, 55, 73$

Calculate $48^2 + 55^2 = 2304 + 3025 = 5329$, and $73^2 = 5329$. $5329 = 5329$, this is a triple.

Step4: Test Option 3: $8, 8, \sqrt{31}$

Calculate $8^2 + (\sqrt{31})^2 = 64 + 31 = 95$, and $8^2 = 64$. $95
eq 64$, so not a triple.

Step5: Test Option 4: $20, 21, 30$

Calculate $20^2 + 21^2 = 400 + 441 = 841$, and $30^2 = 900$. $841
eq 900$, so not a triple.

Answer:

B. 48, 55, 73