Question

pre-algebra ic sem 2 fall 2025
finding the hypotenuse in right triangles
what is the length of the hypotenuse of the triangle?
√33 ft
√22 ft
√65 ft
√57 ft
56:31

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle \(ABC\) with legs \(a = 4\) and \(b=7\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Substitute \(a = 4\) and \(b = 7\) into the formula: \(c^{2}=4^{2}+7^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(4^{2}=16\) and \(7^{2}=49\). Then \(c^{2}=16 + 49\).

Step3: Simplify the right - hand side

\(16+49 = 65\), so \(c^{2}=65\).

Step4: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length of a side of a triangle), \(c=\sqrt{65}\).

Answer:

\(\sqrt{65}\text{ ft}\)