Question

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

Explanation:

Step1: Recall Pythagorean Theorem

For a right - triangle, the Pythagorean theorem states that \(c^{2}=a^{2}+b^{2}\), where \(c\) is the length of the hypotenuse and \(a\) and \(b\) are the lengths of the other two sides.
Here, \(a = 5\space\text{cm}\) and \(b=3\space\text{cm}\).

Step2: Substitute values into the formula

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

Step3: Solve for \(c\)

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

Answer:

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