PART 1:
Question 1:
Start with a rectangle with dimensions in the ratio 2:1. What side length do you need your square to have? How could you construct it?
Solution 1:
rectangle side length will be "a" and "2a" as the ratio is 1:2
Because the lengths are "a" and "2a", to find the area of the rectangle you'll have to do "a x 2a = 2a^2"
Because we are not cutting out any of the rectangle's area, the area of the square must be "2a^2"
To find the side lengths of the square you'll have to do "√(2a^2)" because you have to do "x times x" to find the area (x=√(2a^2)).
PART 2:
Question 2:
Start with a square. How many different ways can you find to cut it into two pieces to make a rectangle? Or three pieces?
Solution 2:
Is shown in the attached file.