Question

aaliyah correctly used the diagram shown to explain the pythagorean theorem to a classmate. which statement did aaliyah use in her expianation?
a. ( 3^{2}+4^{2}>5^{2} )
b. ( 5^{2}+5^{2}<3^{2} )
c. ( 5^{2}+5^{2}=3^{2} )
d. ( 3^{2}+4^{2}=5^{2} )

Explanation:

Step1: Calculate each side of the equation for option A

For \(3^{2}+4^{2}\), \(3^{2}=9\), \(4^{2} = 16\), so \(3^{2}+4^{2}=9 + 16=25\). And \(5^{2}=25\). So \(3^{2}+4^{2}=5^{2}\), not \(3^{2}+4^{2}>5^{2}\).

Step2: Calculate each side of the equation for option B

For \(5^{2}+5^{2}\), \(5^{2}=25\), so \(5^{2}+5^{2}=25+25 = 50\). And \(3^{2}=9\). So \(5^{2}+5^{2}>3^{2}\), not \(5^{2}+5^{2}<3^{2}\).

Step3: Calculate each side of the equation for option C

For \(5^{2}+5^{2}=50\) and \(3^{2}=9\). So \(5^{2}+5^{2}
eq3^{2}\).

Step4: Calculate each side of the equation for option D

For \(3^{2}+4^{2}\), \(3^{2}=9\), \(4^{2}=16\), so \(3^{2}+4^{2}=9 + 16=25\). And \(5^{2}=25\). So \(3^{2}+4^{2}=5^{2}\), which is in line with the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (\(a = 3\), \(b = 4\), \(c = 5\)).

Answer:

D. \(3^{2}+4^{2}=5^{2}\)