Question

if the legs of a right triangle are 3 feet and 4 feet, the length of the hypotenuse is _______ feet. a) 9 b) 25 c) 5 d) 16

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 3\) and \(b = 4\), and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\).
Substitute \(a = 3\) and \(b = 4\) into the formula: \(3^{2}+4^{2}=c^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(3^{2}=9\), \(4^{2}=16\). Then \(a^{2}+b^{2}=9 + 16=25\). So \(c^{2}=25\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length of a side), \(c=\sqrt{25}=5\).

Answer:

C. 5