Answer to Question #165107 in Geometry for April joy Quila

Question

You are interesting in a buying a gift that is shaped like a cube for your fruend.However,you only have a 5 square yards of wrapping paper.the formula is s=√A-6 where s is the edge length,and A is the surface area.What is the longest side length of a cube you could buy based on how much wrapping paper you have?round your answer to the nearest tenth of a yard?

Answer 1

$\displaystyle s = \sqrt{\frac{A}{6}} \\ s^2 =\frac{A}{6} \\ A = 6s^2 \\ 6s^2 \leq 5 \\ 6s^2 - 5 \leq 0\\ s^2 - \frac{5}{6} \leq 0 \\ \left(s - \sqrt{\frac{5}{6}}\right)\left(s - \sqrt{\frac{5}{6}}\right) \leq 0 \\ -\sqrt{\frac{5}{6}} \leq s \leq \sqrt{\frac{5}{6}} \\ \therefore \textsf{The longest side length of a cube you}\\ \textsf{could buy based on how much wrapping}\\ \textsf{paper you have is}\,\,\, 0.9\,\,\textsf{yards}\,\, (\textsf{to nearest tenth}).$