Final answer:
Applying the 45º-45º-90º Triangle Theorem, the length of each leg of a right triangle with a hypotenuse of 10 inches is 5√2 inches.
Step-by-step explanation:
Applying the 45º-45º-90º Triangle Theorem, also known as the isosceles right triangle theorem, we can determine the length of a leg of a right triangle when the hypotenuse is given.
In this special triangle, the lengths of the legs are equal, and each leg is √2 times shorter than the hypotenuse. If the hypotenuse (c) is 10 inches, then each leg (a and b) can be found using the formula:
a = b = c/√2
Plugging in the value of the hypotenuse:
a = b = 10/√2
To rationalize the denominator, we multiply by √2/√2 and get:
a = b = (10√2)/2
Now we simplify:
a = b = 5√2 inches
Thus, the length of each leg of the right triangle is 5√2 inches.