Question

1. if you construct a right triangle and accurately measure the lengths of its two legs a and b and its hypotenuse c, which of the following calculations would you perform with these lengths to verify the pythagorean theorem?

the correct option was a
check if a² + b² = c²?
check if a + b = c
check if a × b = c
check if a² - b² = c²?

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem states that for a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\).

Step2: Analyze each option

• Option “Check if \(a + b=c\)”: This is incorrect. For example, if \(a = 3\), \(b = 4\), \(c=5\), \(a + b=3 + 4=7

eq5\).

• Option “Check if \(a\times b=c\)”: Incorrect. Using the same example \(a = 3\), \(b = 4\), \(c = 5\), \(a\times b=3\times4 = 12

eq5\).

• Option “Check if \(a^{2}-b^{2}=c^{2}\)”: Incorrect. For a right - triangle, \(a^{2}+b^{2}=c^{2}\), not \(a^{2}-b^{2}=c^{2}\).
• Option “Check if \(a^{2}+b^{2}=c^{2}\)”: Correct as it is the formula of the Pythagorean theorem.

Answer:

Check if \(a^{2}+b^{2}=c^{2}\)