Question

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

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\).
Here, \(a = 5\space cm\) and \(b=3\space cm\).

Step2: Apply the Pythagorean theorem

Substitute \(a = 5\) and \(b = 3\) into the formula \(c^{2}=a^{2}+b^{2}\).
\(c^{2}=5^{2}+3^{2}\)
\(c^{2}=25 + 9\)
\(c^{2}=34\)

Step3: Solve for \(c\)

Take the square root of both sides to find \(c\). Since \(c\) represents the length of a side of a triangle, we take the positive square root.
\(c=\sqrt{34}\space cm\)

Answer:

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