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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