Given three rectangles, the length and width of the first 5 and 3 cm of the second 5 and 4 cm

| April 11, 2021 | education

Given three rectangles, the length and width of the first 5 and 3 cm of the second 5 and 4 cm of the third 7 and 2 cm is it possible to make a square from these rectangles.

Let’s denote the vertices of the rectangles as follows:

1) ABCD: AB = CD = 5 cm, BC = AD = 3 cm.

2) A1B1C1D1: A1B1 = C1D1 = 5 cm, B1C1 = A1D1 = 4 cm.

3) А2В2С2D2: A2B2 = C2D2 = 7 cm, B2C2 = A2D2 = 2 cm.

If you can make a square from these rectangles, then its area should be equal to the sum of the areas of these rectangles, i.e .:

S = AB * BC + A1B1 * B1 * C1 + A2 * B2 = 5 * 3 + 5 * 4 + 7 * 2 = 49.

Therefore, the side of this square A must be equal to:

S = A * A = 49, A = 7 cm.

Then it becomes clear how to fold a square with a side of 7 cm from these rectangles.

Let’s put ABCD and A1B1C1D1 next to each other so that CD is adjacent to A1B1.

We get a rectangle with a length of 3 + 4 = 7 cm and a width of 5 cm.

If we put a rectangle A2B2C2D2 on top of this rectangle, we get a square with a side of 7 cm.



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