Final answer:
The length of diagonal AC of the square with a side extension BE of 6 cm is √(6² + 6²), which simplifies to 6√2 cm.
Step-by-step explanation:
The student has asked about determining the length of the diagonal AC of a square given the length of a side extension BE which is 6 cm. In a square, the diagonal can be found using the Pythagorean theorem, where the diagonal acts as the hypotenuse of two congruent right-angle triangles formed by the diagonal of the square.
Since the square has all sides equal, if one side is 6 cm (given that BE equals 6 cm and assuming BE is the extension of the side AB of the square), then each side of the square is also 6 cm.
Using the Pythagorean theorem, which states that in a right-angled 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, the length of diagonal AC would therefore be:
AC = √(AB² + BC²) = √(6² + 6²) = √(36 + 36) = √72 = 6√2 cm
This calculation assumes that the length of BE gives us the length of one side of the square because BE is the extension of side AB. If that assumption is correct, the length of diagonal AC in square ABCD is 6√2 cm.