Question

determine if each of the following sets of numbers could or could not make a right triangle.
select the correct option for each set of numbers.

numbers	right triangle	not a right triangle
(72, 21, 75)	✔
(195, 291, 216)	✔

Explanation:

Step1: Recall Pythagorean Theorem

For a right triangle, \(a^2 + b^2 = c^2\) (where \(c\) is the longest side).

Step2: Check {48, 73, 55}

Longest side \(c = 73\). Calculate \(48^2 + 55^2\):
\(48^2 = 2304\), \(55^2 = 3025\), sum \(= 2304 + 3025 = 5329\).
\(73^2 = 5329\). So \(48^2 + 55^2 = 73^2\) → Right Triangle.

Step3: Check {72, 21, 75}

Longest side \(c = 75\). Calculate \(72^2 + 21^2\):
\(72^2 = 5184\), \(21^2 = 441\), sum \(= 5184 + 441 = 5625\).
\(75^2 = 5625\). So \(72^2 + 21^2 = 75^2\) → Right Triangle.

Step4: Check {195, 291, 216}

Longest side \(c = 291\). Calculate \(195^2 + 216^2\):
\(195^2 = 38025\), \(216^2 = 46656\), sum \(= 38025 + 46656 = 84681\).
\(291^2 = 84681\). So \(195^2 + 216^2 = 291^2\) → Right Triangle.

Answer:

All sets \(\{48, 73, 55\}\), \(\{72, 21, 75\}\), \(\{195, 291, 216\}\) form right triangles (as verified by Pythagorean Theorem).