# The two rectangles have the same area. The length of the first rectangle is 0.6 m and the width is 4 dm.

The two rectangles have the same area. The length of the first rectangle is 0.6 m and the width is 4 dm. What is the length of the second rectangle if it is 30 cm wide? Find and compare the perimeters of these rectangles.

1) Let’s express all the values ​​in meters: 4 dm = 0.4 m, 30 cm = 0.3 m;

2) Determine the area of ​​a rectangle with known values: S = a b = 0.6 0.4 = 0.24 (dm ^ 2). This value of the area will also apply (according to the problem statement) to the second rectangle.

3) Knowing the area of ​​the second rectangle and its width, we determine what its length is equal to: a = S: b = 0.24: 0.3 = 0.8 (m);

4) Calculate the perimeter of the first rectangle using the formula: P = (a + b) 2 = (0.6 + 0.4) 2 = 2 (m);

5) Find the perimeter of the second rectangle by the formula: P = (a + b) 2 = (0.3 + 0.8) 2 = 2.2 (m);

6) 2.2 m ˃ 2 m, which means that the perimeter of the second rectangle is greater than the perimeter of the first rectangle.

Answer: the length of the second rectangle is 0.8 m; the perimeter of the second rectangle is greater than the perimeter of the first rectangle.

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