Question

jennies math tutor drew three lines to create a right angle scalene triangle in her math notebook. which of the following are the possible whole number lengths of the three segments? 33,35,48 2,3,4 7,24,25 16,17,23

Explanation:

Step1: Recall the Pythagorean theorem

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

Step2: Check each option

• Option \([2,3,4]\):

\(2^{2}+3^{2}=4 + 9=13\), and \(4^{2}=16\). Since \(13
eq16\), this is not a right - triangle.

• Option \([7,24,25]\):

\(7^{2}+24^{2}=49+576 = 625\), and \(25^{2}=625\). So \(7^{2}+24^{2}=25^{2}\).

• Option \([16,17,23]\):

\(16^{2}+17^{2}=256 + 289=545\), and \(23^{2}=529\). Since \(545
eq529\), this is not a right - triangle.

• Option \([33,35,48]\):

\(33^{2}+35^{2}=1089+1225 = 2314\), and \(48^{2}=2304\). Since \(2314
eq2304\), this is not a right - triangle.

Answer:

\([7,24,25]\)