The Correct answer is 6√2 inches

Explanation

1. Formula:

c^2 = a^2 + b^2

where:

c is the hypotenuse (12 inches in this case)
a and b are the lengths of the legs (which are equal in an isosceles triangle)

2. Substituting known values:

We know c = 12 and we want to find a (which is equal to b). So, the equation becomes:

12^2 = a^2 + a^2

3. Combining like terms:

12^2 = 2a^2

4. Isolating a:

To solve for a, we need to get it by itself. Divide both sides by 2:

12^2 / 2 = a^2

5. Taking the square root:

Since we're dealing with squared values, we need to take the square root of both sides to find the actual length of a:

sqrt(12^2 / 2) = sqrt(a^2)

6. Simplifying:

6√2 = a

Therefore, the length of each leg in the isosceles right triangle is 6√2 inches.

What is the Pythagorean theorem?

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 (called legs).

Formula:

The relationship between the sides of a right triangle can be expressed mathematically using the following formula:

c^2 = a^2 + b^2

where:

• c represents the length of the hypotenuse (longest side)
• a and b represent the lengths of the other two sides (legs)