Step 1: Understand that in a square, the diagonals are equal in length and they bisect each other at 90 degrees. This forms two right-angled triangles within the square.

Step 2: We know the length of the diagonal is 10 cm. We can use the Pythagorean theorem to find the length of the sides of the square. The Pythagorean theorem 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. In this case, the hypotenuse is the diagonal of the square.

Step 3: Let's denote the sides of the square as 'a'. So, according to the Pythagorean theorem, we have a^2 + a^2 = 10^2.

Step 4: Simplify the equation to 2a^2 = 100.

Step 5: Solve for 'a' by dividing both sides of the equation by 2 to get a^2 = 50.

Step 6: Take the square root of both sides to solve for 'a'. So, a = √50 = 7.07 cm (rounded to the nearest tenth).

Step 7: The perimeter of a square is given by the formula 4a. Substituting the value of 'a' we found, the perimeter is 4 * 7.07 = 28.3 cm (rounded to the nearest tenth).

Question

Step 1: Understand that in a square, the diagonals are equal in length and they bisect each other at 90 degrees. This forms two right-angled triangles within the square.

Step 2: We know the length of the diagonal is 10 cm. We can use the Pythagorean theorem to find the length of the sides of the square. The Pythagorean theorem 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. In this case, the hypotenuse is the diagonal of the square.

Step 3: Let's denote the sides of the square as 'a'. So, according to the Pythagorean theorem, we have a^2 + a^2 = 10^2.

Step 4: Simplify the equation to 2a^2 = 100.

Step 5: Solve for 'a' by dividing both sides of the equation by 2 to get a^2 = 50.

Step 6: Take the square root of both sides to solve for 'a'. So, a = √50 = 7.07 cm (rounded to the nearest tenth).

Step 7: The perimeter of a square is given by the formula 4a. Substituting the value of 'a' we found, the perimeter is 4 * 7.07 = 28.3 cm (rounded to the nearest tenth).

Knowee AI · Accepted Answer

Step 1: Understand that in a square, the diagonals are equal in length and they bisect each other at 90 degrees. This forms two right-angled triangles within the square.

Step 2: We know the length of the diagonal is 10 cm. We can use the Pythagorean theorem to find the length of the sides of the square. The Pythagorean theorem 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. In this case, the hypotenuse is the diagonal of the square.

Step 3: Let's denote the sides of the square as 'a'. So, according to the Pythagorean theorem, we have a^2 + a^2 = 10^2.

Step 4: Simplify the equation to 2a^2 = 100.

Step 5: Solve for 'a' by dividing both sides of the equation by 2 to get a^2 = 50.

Step 6: Take the square root of both sides to solve for 'a'. So, a = √50 = 7.07 cm (rounded to the nearest tenth).

Step 7: The perimeter of a square is given by the formula 4a. Substituting the value of 'a' we found, the perimeter is 4 * 7.07 = 28.3 cm (rounded to the nearest tenth).

Find the perimeter of a square with diagonal 10 centimeters. Round to the nearest tenth.

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