Question

do these measurements form a right triangle? side 1: $3\sqrt{91}$ side 2: 24 side 3: 15 show your work here hint to add the square root symbol ($\sqrt{\square}$), type
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Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\) where \(c\) is the longest side. Here, longest side is \(3\sqrt{91}\), so check if \(15^2 + 24^2=(3\sqrt{91})^2\).

Step2: Calculate left - hand side (LHS)

\(15^2+24^2 = 225 + 576=801\)

Step3: Calculate right - hand side (RHS)

\((3\sqrt{91})^2=3^2\times(\sqrt{91})^2 = 9\times91 = 819\)

Step4: Compare LHS and RHS

Since \(801
eq819\), the Pythagorean theorem is not satisfied.

Answer:

No, these measurements do not form a right triangle.