Final Answer:
The perimeter of the square is 70–√ inches, and the area is 1225 square inches.
Step-by-step explanation:
To find the perimeter of the square, we need to sum up the lengths of all four sides. In a square, the diagonal divides it into two congruent right-angled triangles. The diagonal, side length (s), and the Pythagorean theorem are related by the equation (s² + s² = d² ), where (d) is the diagonal length. In this case, the diagonal length is (35–√) inches.
By substituting the given value into the equation, we get (s² + s² = (35–√)² ). Solving for (s), we find (s = {35–√} / {√2}). Since the perimeter is the sum of all four sides, we multiply the side length by 4: (P = 4s). Simplifying, we arrive at the final answer for the perimeter: (70–√) inches.
To calculate the area of the square, we use the formula (A = s² ). Substituting the expression for (s) from the Pythagorean theorem, we get A = ({35–√} / {√2})². Simplifying this expression gives the final answer for the area: (1225) square inches.
In summary, the perimeter of the square is (70–√) inches, and the area is (1225) square inches, both derived through the Pythagorean theorem and the formulae for perimeter and area of a square.