Final answer:
To find the length of the diagonal of a square, we can use the Pythagorean theorem. Given that the square has an area of 121 square units, we can find the length of one side by taking the square root of 121. Using the formula for the Pythagorean theorem, we can calculate the length of the diagonal of the square to be approximately 15.6 units.
Step-by-step explanation:
To find the length of the diagonal of a square, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In a square, the two sides and the diagonal form a right triangle. Let's assume the length of one side of the square is x. To find the length of the diagonal, we can use the formula:
diagonal^2 = x^2 + x^2
As the square has an area of 121 square units, we can determine the length of one side by taking the square root of 121, which is 11. Therefore, x = 11.
Substituting the value of x into the formula, we get:
diagonal^2 = 11^2 + 11^2
diagonal^2 = 121 + 121
diagonal^2 = 242
Taking the square root of both sides, we find:
diagonal = √242
Using a calculator, we can approximate the value of the square root of 242 to the nearest tenth, which is 15.6.