Question

which is the length of the hypotenuse of the triangle?
√214 ft
√94 ft
37 ft
33 ft

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 12\) ft and \(b=35\) ft, and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
Substitute \(a = 12\) and \(b = 35\) into the formula: \(c^{2}=12^{2}+35^{2}\).
Calculate \(12^{2}=144\) and \(35^{2}=1225\). Then \(c^{2}=144 + 1225\).

Step2: Calculate \(c^{2}\) and \(c\)

\(c^{2}=144+1225=1369\).
Take the square root of both sides: \(c=\sqrt{1369}\).
Since \(37\times37 = 1369\), \(c = 37\) ft.

Answer:

\(37\) ft