Question

given the triangle below, what is the length of the hypotenuse?
3 cm
5 cm
a 15 cm
b √34 cm
c √15 cm
d 8 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 5\), and \(c\) is the hypotenuse.
$$3^{2}+5^{2}=c^{2}$$

Step2: Calculate \(3^{2}+5^{2}\)

\(3^{2}=9\), \(5^{2}=25\). Then \(9 + 25=c^{2}\), so \(c^{2}=34\).

Step3: Solve for \(c\)

Take the square root of both sides. \(c=\sqrt{34}\) (since length \(c>0\)).

Answer:

B. \(\sqrt{34}\) cm