what is the length of the hypotenuse, x, if (12, 35, x) is a pythagorean triple?\n33\n37\n47\n58

Answer

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides (a), (b) and hypotenuse (c), (a^{2}+b^{2}=c^{2}). In a Pythagorean triple ((12,35,x)), if (a = 12) and (b = 35), then (x) (the hypotenuse) satisfies (12^{2}+35^{2}=x^{2}).

Step2: Calculate (12^{2}) and (35^{2})

(12^{2}=12\times12 = 144) and (35^{2}=35\times35=1225).

Step3: Find the sum

(12^{2}+35^{2}=144 + 1225=1369). So (x^{2}=1369).

Step4: Solve for (x)

Take the square - root of both sides. Since (x) represents the length of a side of a triangle (a non - negative quantity), (x=\sqrt{1369}=37).