Final answer:
The value of 'r' in the isosceles triangle can be found using the Pythagorean theorem by calculating the square root of the sum of the squares of the other two sides, resulting in r = √(4² + 6²) = √52.
Step-by-step explanation:
The value of r in an isosceles triangle can be found using the Pythagorean theorem if you know the lengths of the triangle's sides. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). For an isosceles triangle with sides of length 4 and 6, you would use the equation r = √(4² + 6²) to solve for the hypotenuse r. Plugging the values in, we get r = √(16 + 36) = √52, which simplifies to a numerical value through further calculation.