Grade 10 Quadratic Word Problems - number problems and open topped boxes

Setting up word problems and solving using the quadratic formula. Some problems ask you to solve for a value, others ask you to find a minimum, or maximum. You should understand the difference in what is being asked and know whether you are trying to find the zeros (or x-intercepts), or if you are finding the x coordinate of the vertex.
1. 3 x the square of an integer is 432, Find the two numbers.
2. the product of 2 consecutive even numbers is 288, what are the numbers
3. The sum of 2 numbers is 26. The sum of their squares is a minimum.
4. Find the length of a square cut out of an open topped box given the area of its base.
5. Find the length of the sides of a right triangle given the hypotenuse and that one side is 2 m longer than the other.