Question

can you identify each missing side as a leg or a hypotenuse? leg or hypotenuse? 35 84 x

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Here, let the legs be 35 and 84, and the hypotenuse be \(x\).

Step2: Apply the formula

\(35^{2}+84^{2}=x^{2}\). Calculate \(35^{2}=35\times35 = 1225\) and \(84^{2}=84\times84=7056\). Then \(1225 + 7056=x^{2}\), so \(x^{2}=8281\).

Step3: Solve for \(x\)

Take the square - root of both sides. Since \(x\) represents the length of a side of a triangle, \(x=\sqrt{8281}=91\). And \(x\) is the hypotenuse as it is opposite the right - angle.

Answer:

\(x = 91\) and \(x\) is the hypotenuse.