Question

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

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 theorem

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

Step3: Find the value of \(x\)

Take the square - root of both sides. \(x=\sqrt{8281}=91\). Since the hypotenuse is the longest side in a right - triangle, and we used the Pythagorean theorem with the two given sides as legs, \(x\) is the hypotenuse.

Answer:

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