Question

look at the graphic. which equation is verified by the graphic? a ( 5^{2}+13^{2}=12^{2} ) b ( 5 + 12 = 17 ) c ( 5^{2}+12^{2}=13^{2} ) d ( sqrt{25}+sqrt{144}=sqrt{169} )

Explanation:

Step1: Count the squares

Count the number of small squares in each side - related square. The smaller square has \(5\times5 = 25\) small squares (\(a = 5\)), the medium - sized square has \(12\times12=144\) small squares (\(b = 12\)), and the largest square has \(13\times13 = 169\) small squares (\(c = 13\)).

Step2: Apply the Pythagorean theorem

The Pythagorean theorem states that for a right - triangle \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. Substitute \(a = 5\), \(b = 12\), and \(c = 13\) into the formula:

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So \(5^{2}+12^{2}=13^{2}\)

Answer:

C. \(5^{2}+12^{2}=13^{2}\)