Use a piece of rectangular paper 15 cm long and 7 cm wide to cut out the largest square. What is the area of the largest square? How many square centimeters are left?

Maximum square area = 7 × 7 = 49 square centimeters
Total area = 15 × 7 = 105 square centimeter
Remaining area = 105-49 = 56 square centimeters

A square, each side length increases 50 decimeters, the area increases 135 square meters?

135 square meters = 13500 square decimeters
If the length of the original square is x decimeter, then
（x+50)²-x²=13500
x²+100x+2500-x²=13500
100x=11000
x=110
That is: the original square side length is 110 decimeters = 11 meters
Original square area = 11 × 11 = 121 (M2)

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