11. Briond's backsplash in her ki up of squore tiles like the one be are white with a black diggonals the following would help her find of the black stripe? A. \( 4+4=x \) B. \( 4^{2}+4^{2}=x \) C. \( 4^{2}+4^{2}=x^{2} \) D. \( \sqrt{4}+\sqrt{4}=x \)

To find the length of the black stripe in Briond's backsplash, you want to consider the diagonal of a square tile. Since each tile is a square, the relationship between the side length and the diagonal is described by the Pythagorean theorem. If each side is 4, for a square, the diagonal would be calculated using \(4^2 + 4^2 = x^2\) - one of the squared sides plus the other squared side gives you the squared diagonal length. When solving \(4^2 + 4^2 = x^2\), you end up with \(16 + 16 = x^2\) or \(32 = x^2\). This means \(x\) (the diagonal length) would equal \(\sqrt{32}\) which simplifies to \(4\sqrt{2}\). Understanding this will not only help Briond figure out the length of her black stripe, but will also enhance her overall design knowledge!