Calling all mathematicians!

[SeeDRankLou]

(This may take a while to type, so someone might post before me)

1. OK, a rectangle with a diagonal is 2 congruent right triangles on top of one another, right? Lets call the sides of the triangle 2a and 3a (the ratio, 2 of something to 3 of something), which are also two of the sides of the rectangle, and the side opposite the right angle is 26cm, the diagonal. Simple Pythagorean Theorem, (2a)^2 + (3a)^2 = 26^2. Work it out, a=52, so the sides are 104cm and 156cm, and thus the perimeter is 520cm.

2. Ok, a cube has all the same sides. Volume of a cube = length times width times height. Since those are all the same, let's just call them all "a". So a^3 = 10cm^3. a = (cube root)(10)cm. There are 12 sides to a cube, so the sum of the lengths of the edges = 12(cube root)(10)cm. There are six sides to a cube. Each side of a cube is a square, and the area of a square = length times width, so the surface area of a cube = 6 times length time width. So surface area = 6a^2 = 6 x 10^(2/3)cm.