Question

determine whether each triangle with sides of given lengths is a right triangle. justify your answer. (example 3) 4. 28 yd, 195 yd, 197 yd 5 30 cm, 122 cm, 125 cm

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Check the first set of side - lengths (28 yd, 195 yd, 197 yd)

Calculate \(28^{2}+195^{2}\):

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And \(197^{2}=197\times197 = 38809\). Since \(28^{2}+195^{2}=197^{2}\), it is a right - triangle.

Step3: Check the second set of side - lengths (30 cm, 122 cm, 125 cm)

Calculate \(30^{2}+122^{2}\):

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And \(125^{2}=125\times125=15625\). Since \(30^{2}+122^{2}
eq125^{2}\), it is not a right - triangle.

Answer:

The triangle with side - lengths 28 yd, 195 yd, 197 yd is a right - triangle. The triangle with side - lengths 30 cm, 122 cm, 125 cm is not a right - triangle.