Final answer:
To find the length of the hypotenuse in a right triangle with both perpendicular sides measuring 10 feet, use the Pythagorean theorem. The calculation is √(10^2 + 10^2), which simplifies to 10√2 feet.
Step-by-step explanation:
The student has asked how to find the length of the remaining side of a right triangle when the perpendicular sides are both 10 feet long. This problem can be solved using the Pythagorean theorem, which relates the lengths of the legs of a right triangle with its hypotenuse.
According to the Pythagorean theorem, for a right triangle with sides of lengths a and b and hypotenuse c, the relationship is a² + b² = c². Therefore, to find the hypotenuse, we use the formula c = √(a² + b²).
Substituting the given lengths:
We calculate:
c = √(10^2 + 10^2) = √(100 + 100) = √200
In simplified radical form, c = √(100 × 2) = 10√2 feet. Hence, the length of the hypotenuse is 10√2 feet.