Question

pythagorean unit practice
which measurements could not represent the side lengths of a right triangle?
a 12 cm, 35 cm, 37 cm
b 6 cm, 8 cm, 10 cm
c 10 cm, 24 cm, 26 cm
d 4 cm, 6 cm, 10 cm

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check option A

For \(a = 12\), \(b = 35\), \(c = 37\). Calculate \(a^{2}+b^{2}=12^{2}+35^{2}=144 + 1225=1369\) and \(c^{2}=37^{2}=1369\). So, it can be side - lengths of a right - triangle.

Step3: Check option B

For \(a = 6\), \(b = 8\), \(c = 10\). Calculate \(a^{2}+b^{2}=6^{2}+8^{2}=36 + 64 = 100\) and \(c^{2}=10^{2}=100\). So, it can be side - lengths of a right - triangle.

Step4: Check option C

For \(a = 10\), \(b = 24\), \(c = 26\). Calculate \(a^{2}+b^{2}=10^{2}+24^{2}=100+576 = 676\) and \(c^{2}=26^{2}=676\). So, it can be side - lengths of a right - triangle.

Step5: Check option D

For \(a = 4\), \(b = 6\), \(c = 10\). Calculate \(a^{2}+b^{2}=4^{2}+6^{2}=16 + 36=52\) and \(c^{2}=10^{2}=100\). Since \(a^{2}+b^{2}
eq c^{2}\), it cannot be side - lengths of a right - triangle.

Answer:

D. 4 cm, 6 cm, 10 cm