10. if the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square?
10. if the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square?
Answer
Explanation:
Step1: Find the side length of the square
Let the side length of the square be (a). According to the Pythagorean theorem, for a square with diagonal (d), (d^{2}=a^{2}+a^{2}=2a^{2}). Given (d = 11.3) meters, then (a^{2}=\frac{d^{2}}{2}=\frac{11.3^{2}}{2}=\frac{127.69}{2}=63.845), and (a=\sqrt{63.845}\approx 8) meters.
Step2: Calculate the perimeter of the square
The perimeter formula of a square is (P = 4a). Substituting (a\approx8) meters into the formula, we get (P=4\times8 = 32) meters.
Answer:
32 meters