Question

which figure verifies the pythagorean theorem? a 12 8 10 b 5 4 6 c 15 6 10 d 5 12 13

Explanation:

Step1: Recall the Pythagorean Theorem

The Pythagorean Theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side) and \(a\) and \(b\) are the other two sides.

Step2: Check option A

Let \(a = 8\), \(b = 10\), \(c = 12\). Then \(a^{2}+b^{2}=8^{2}+10^{2}=64 + 100=164\) and \(c^{2}=12^{2}=144\). Since \(164
eq144\), option A is incorrect.

Step3: Check option B

Let \(a = 4\), \(b = 5\), \(c = 6\). Then \(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25 = 41\) and \(c^{2}=6^{2}=36\). Since \(41
eq36\), option B is incorrect.

Step4: Check option C

Let \(a = 6\), \(b = 10\), \(c = 15\). Then \(a^{2}+b^{2}=6^{2}+10^{2}=36+100 = 136\) and \(c^{2}=15^{2}=225\). Since \(136
eq225\), option C is incorrect.

Step5: Check option D

Let \(a = 5\), \(b = 12\), \(c = 13\). Then \(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144=169\) and \(c^{2}=13^{2}=169\). Since \(5^{2}+12^{2}=13^{2}\), option D satisfies the Pythagorean Theorem.

Answer:

D