Question

find the length of the hypotenuse.
6 in
8 in
?
10 in
100 in
14 in
5.29 in

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, the Pythagorean theorem is given by \(c^{2}=a^{2}+b^{2}\), where \(a\) and \(b\) are the lengths of the legs of the right - triangle and \(c\) is the length of the hypotenuse. Here, \(a = 6\) in and \(b=8\) in.

Step2: Substitute values into the formula

Substitute \(a = 6\) and \(b = 8\) into the formula: \(c^{2}=6^{2}+8^{2}\). Calculate \(6^{2}=36\) and \(8^{2}=64\). Then \(c^{2}=36 + 64\).

Step3: Simplify the right - hand side

\(36+64 = 100\), so \(c^{2}=100\).

Step4: Solve for c

Take the square root of both sides. Since \(c\) represents the length of a side of a triangle, we take the positive square root. So \(c=\sqrt{100}=10\) in.

Answer:

A. 10 in