The perimeter of a rectangular lawn is 36m. If its length and width increase by 3M, how many square meters will the original lawn area increase?

The perimeter of a rectangular lawn is 36m. If its length and width increase by 3M, how many square meters will the original lawn area increase?

36 △ 2 × 3 + 3 × 3 = 63 (M2)
It is equivalent to adding a rectangle on the long side, which is 3 meters wide, and adding a rectangle on the wide side, which is also 3 meters wide. The sum of their areas is 36 △ 2 × 3, and the joint is a square with an area of 3 × 3

How much is the perimeter of the original rectangular lawn

If the length of the rectangle is a meter and the width is B meter, the increased area is
（a+3）（b+3）
=ab+3（a+b）+9
If the original area is ab, then 3 (a + b) + 9 = 159
The solution is a + B = 50m
Then the perimeter of the original rectangle is 2 (a + b) = 2 × 50 = 100m

The perimeter of a rectangular lawn is 36m. If its length and width are increased by 3M, how many meters will the lawn area be increased

If the length is x, then the width is (36-2x) / 2 = 18-x, and the area is x * (18-x) = 18x-x ^ 2. After 3 meters, the length and width become x + 3 and (18-x + 3) = 21-x, and the area is (x + 3) * (21-x) = 18x-x ^ 2 + 21 * 3 = 18x-x ^ 2 + 63, so the increased area is (18x-x ^ 2 + 63) - (18x-x ^ 2) = 63. I wish you progress and happy life