Question

First, ABCD is a square D = 90 (given) In square ABCD AD and DC are adjacent sides, and AC is diagonal of square then.. AC² = AD² + DC² since ABCD is a square, AD= DC (all sides of the square are equal) ---; (18.79)² =17² + 7² 353.06 = 289+289 - 353.06a 578 so it contradicts that the diagonal of the square is equal to the root of the square with two sides.

Answer 1

The student's question involves the Pythagorean theorem applied to a square, incorrectly using disparate side lengths. The theorem correctly calculates the diagonal of a square from the length of its sides.

Step-by-step explanation:

The student's question relates to the Pythagorean theorem which is a fundamental concept in mathematics, specifically in geometry. The Pythagorean theorem states that in a right-angled 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). The theorem is expressed as a² + b² = c². When applied to a square's diagonal and its sides, the diagonal measures √(AD² + DC²) because all sides of a square are of equal length.

An error occurs in the student's example where it is stated '18.79² = 17² + 7²', which suggests a non-square rectangle. However, for a square with equal side lengths, the correct application of the Pythagorean theorem would result in the diagonal being equal to the square root of the sum of the squares of either of its two adjacent sides.