The authority of primary school olympiad network released three knowledge points of olympiad geometry. For more information about these three knowledge points, please visit the Primary School Olympiad Network. There is no secret to leadership success, if there is one, there are two: the first is to stick to the end and never give up; The second is when you want to give up, look back at the first secret, stick to it and never give up. Learning also needs more practice. The following is the "Three Knowledge Points of Olympiad Geometry" compiled by Da Fanwen. For your reference.

First article

Exercise: If the width of a rectangle remains the same and its length is increased by 6 meters, its area will increase by 54 square meters. If the width is reduced by 3 meters, its area will be reduced by 36 square meters. What is the original area of this rectangle?

Answer and analysis: From: "If the width is unchanged and the length increases by 6 meters, its area will increase by 54 square meters", we can know that its width is 54÷6=9 (meters); From "the length is constant, the width is reduced by 3m, so its area is reduced by 36m", we can know that its length is 36÷3= 12 (m), so the area of this rectangle is 12x9 = 108 (m). (36÷3)×(54÷9)= 108 (square meter)

Exercise (1): If the width of a rectangle is unchanged and the length is reduced by 3 meters, its area will be reduced by 24 square meters; If the length remains the same and the width increases by 4 meters, its area will increase by 60 square meters. What is the original area of this rectangle?

Exercise (2): If the width of a rectangle remains the same, its length will be increased by 5 meters, and its area will be increased by 30 square meters; If the width increases by 3 meters, its area will increase by 48 square meters. How many square meters is this rectangle?

Exercise (3): If the length of a rectangle is reduced by 3 meters, or the width is reduced by 2 meters, its area will be reduced by 36 square meters. Find the original area of this rectangle.

The second article

Exercise: The playground of Renmin Road Primary School is 90 meters long and 45 meters wide. After transformation, the length is increased by10m, and the width is increased by 5m. How many square meters has the playground area increased now?

Answer and analysis: subtract the original area of the playground from the current area of the playground to get the increased area. The current area of the playground is (90+ 10)×(45+5)=5000 (square meters), and the original area of the playground is: 90×45=4050 (square meters). So now it is 5000-4050=950 square meters more than before. (90+10) × (45+5)-(90× 45) = 950 (square meter)

Exercise (1): There is a rectangular board with a length of 22 decimeters and a width of 8 decimeters. If the length and width are reduced by 10 decimeter and 3 decimeter respectively, how many square decimeters will the area be reduced?

Exercise (2): A rectangular piece of land, 80 meters long and 45 meters wide. If the width is increased by 5 meters, how many meters should the length be reduced to keep the area unchanged?

The third article

Exercise: The playground of Renmin Road Primary School is 90 meters long and 45 meters wide. After transformation, the length is increased by10m, and the width is increased by 5m. How many square meters has the playground area increased now?

Answer and analysis: subtract the original area of the playground from the current area of the playground to get the increased area. The current area of the playground is (90+ 10)×(45+5)=5000 (square meters), and the original area of the playground is: 90×45=4050 (square meters). So now it is 5000-4050=950 square meters more than before. (90+10) × (45+5)-(90× 45) = 950 (square meter)

Exercise (1): There is a rectangular board with a length of 22 decimeters and a width of 8 decimeters. If the length and width are reduced by 10 decimeter and 3 decimeter respectively, how many square decimeters will the area be reduced?

Exercise (2): A rectangular piece of land, 80 meters long and 45 meters wide. If the width is increased by 5 meters, how many meters should the length be reduced to keep the area unchanged?