Question

1. which set of numbers could be the lengths of the sides of a right triangle?
2. 16,24,28
3. 12,16,20
4. 3,4,6
5. 4,7,8

a) which set of numbers does not represent the sides of a right triangle?

1. 6,8,10
2. 8,15,17
3. 18,24,30
4. 15,30,35
5. determine algebraically if the triangle shown below can be classified as a right triangle.

Explanation:

Step1: Recall the Pythagorean theorem

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 \((4,7,8)\)

\(4^{2}+7^{2}=16 + 49=65\), and \(8^{2}=64\). Since \(4^{2}+7^{2}
eq8^{2}\).

Step3: Check option B \((1,4,6)\)

\(1^{2}+4^{2}=1 + 16=17\), and \(6^{2}=36\). Since \(1^{2}+4^{2}
eq6^{2}\).

Step4: Check option C \((12,16,20)\)

\(12^{2}+16^{2}=144+256 = 400\), and \(20^{2}=400\). Since \(12^{2}+16^{2}=20^{2}\).

Step5: Check option D \((16,24,28)\)

\(16^{2}+24^{2}=256+576 = 832\), and \(28^{2}=784\). Since \(16^{2}+24^{2}
eq28^{2}\).

Answer:

C. \((12,16,20)\)