Question

what is the length of the hypotenuse of the triangle? √40 cm √58 cm √20 cm √23 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle \(ABC\) with legs \(BC = 3\) cm and \(AC=7\) cm and hypotenuse \(AB\), the Pythagorean theorem states that \(AB^{2}=BC^{2}+AC^{2}\).
So, \(AB^{2}=3^{2}+7^{2}\).

Step2: Calculate \(BC^{2}+AC^{2}\)

\(3^{2}=9\) and \(7^{2} = 49\). Then \(BC^{2}+AC^{2}=9 + 49=58\).

Step3: Find the length of the hypotenuse

Since \(AB^{2}=58\), then \(AB=\sqrt{58}\) cm.

Answer:

\(\sqrt{58}\) cm