What is the length of the hypotenuse if two sides of a triangle are 10 inches long?

To find the length of the hypotenuse in a right triangle when both sides are equal, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

If both sides are 10 inches, the calculation would be:

[

c^2 = a^2 + b^2

]

Here, both ( a ) and ( b ) are 10 inches. Hence, the calculation becomes:

[

c^2 = 10^2 + 10^2 = 100 + 100 = 200

]

To find ( c ), which is the hypotenuse, take the square root of 200:

[

c = \sqrt{200} = \sqrt{100 \times 2} = 10\sqrt{2} \approx 14.14 \text{ inches}

]

Therefore, the correct length of the hypotenuse should be approximately 14.14 inches, which is not 4.4 inches, 10 inches, or 15 inches.

The correct answer is