Lisa, a child with strange requirements for her projects, is making a rectangular cardboard box with square bases. she wants the height of the box to be 3 units greater than the side of the square bases. what should the height be if she wants the surface area of the box to be at least 90 square units while using the least amount of cardboard?

[120 total points] (public health) in one of the largest human experiments ever conducted, in 1954 a randomized controlled trial was run to see whether a vaccine developed by a doctor named jonas salk was effective in preventing paralytic polio. a total of 401,974 children (ages 6–9), chosen to be representative of those who might be susceptible to the disease, were randomized to two groups: 200,745 children (the control group c) were injected with a harmless saline solution (a placebo) and the other 201,229 children (the treatment group t) were injected with salk’s vaccine. what was the point of giving saline solution to the children who didn’t get the vaccine? explain briefly.