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a

Explanation

The question asks for the lengths of the legs of the isosceles triangles formed when both diagonals are drawn in a square with a side length of 8.1. First, let's consider the square with side length s = 8 .2. When both diagonals are drawn, they divide the square into four isosceles triangles.3. The diagonal of the square serves as the hypotenuse for each of these isosceles triangles.4. The length of the diagonal can be calculated using the Pythagorean theorem for a square: Diagonal \text{Diagonal} = s\sqrt{2} .5. For our square with s = 8 , the diagonal length is 8\sqrt{2} .6. The legs of each isosceles triangle are equal in length and can be calculated as follows: Leg lengthDiagonal length \text{Leg length} = \frac{\text{Diagonal length}}{2} = \frac{8\sqrt{2}}{2} = 4\sqrt{2} 7. The length of the legs of the isosceles triangles is 4\sqrt{2} , which corresponds to option a \frac{s\sqrt{2}}{2} .Therefore, the correct answer is option a \frac{s\sqrt{2}}{2} .

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