Question

what is the length of the hypotenuse?
3
4
?
select the best answer

Explanation:

Step1: Identify the triangle type

This is a right - triangle with legs \(a = 3\) and \(b = 4\). We use the Pythagorean theorem, which states that for a right - triangle, \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse.

Step2: Substitute the values of \(a\) and \(b\)

Substitute \(a = 3\) and \(b = 4\) into the formula: \(c^{2}=3^{2}+4^{2}\). Calculate \(3^{2}=9\) and \(4^{2}=16\). Then \(c^{2}=9 + 16=25\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{25}=5\).

Answer:

The length of the hypotenuse is \(5\).