Question

determine if the triangle below is a right triangle. if it is not, compute what the hypotenuse would have to be for the triangle to be a right triangle.

65
97
72

a. no, the hypotenuse should be 98
b. no, the hypotenuse should be 99
c. no, the hypotenuse should be 94
d. yes

please select the best answer from the choices provided

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(a\) and \(b\) are legs, \(c\) is hypotenuse. Here, \(a = 65\), \(b = 72\), check if \(65^2 + 72^2 = 97^2\).

Step2: Calculate \(65^2\), \(72^2\), \(97^2\)

\(65^2 = 4225\), \(72^2 = 5184\), sum: \(4225 + 5184 = 9409\). \(97^2 = 9409\)? Wait, \(97\times97 = 9409\)? Wait, no: \(90\times90 = 8100\), \(90\times7 = 630\), \(7\times90 = 630\), \(7\times7 = 49\), so \((90 + 7)^2 = 90^2 + 2\times90\times7 + 7^2 = 8100 + 1260 + 49 = 9409\). Wait, but \(65^2 + 72^2 = 4225 + 5184 = 9409\), which equals \(97^2\). Wait, but that would mean it is a right triangle. Wait, but let me recalculate: 65 squared is 4225, 72 squared is 5184. 4225 + 5184: 4225 + 5000 = 9225, 9225 + 184 = 9409. 97 squared: 9797. Let's do 100100 = 10000, minus 31002 + 3^2 = 10000 - 600 + 9 = 9409. So 65² + 72² = 97². So the triangle is a right triangle.

Wait, but the options: D is "Yes". So the correct answer is D.

Answer:

D. Yes