A rectangle with sides 4cm and 8cm was cut into two rectangles, one of which turned

| February 9, 2021 | education

A rectangle with sides 4cm and 8cm was cut into two rectangles, one of which turned out to be similar to the original rectangle. Find the coefficient of similarity. Perimeters of similar rectangles. Areas of similar rectangles ..

Find the aspect ratio of the original rectangle:

4/8 = ½.

To get the same ratio between the sides obtained from the original rectangle, it is necessary that the smaller side of the resulting rectangle becomes its smaller side, that is, 4 cm.We find the smaller side:

4 * ½ = 2 cm.

To find the coefficient of similarity of two rectangles, divide the similar sides to each other:

2/4 = ½.

The perimeter of the rectangle is:

P = 2 * (a + b), where a and b are the sides of the rectangle.

Find the perimeter of the original rectangle:

P1 = 2 * (4 + 8) = 24 cm.

Find the perimeter of the resulting rectangle:

P2 = 2 * (2 + 4) = 12 cm.

The area of ​​the rectangle is

S = ab.

Find the area of ​​the original rectangle:

S1 = 4 * 8 = 32 cm².

Find the area of ​​the resulting rectangle:

S2 = 2 * 4 = 8 cm².

Answer: the coefficient of similarity of rectangles is ½, the perimeters of similar rectangles are 12 cm and 24 cm, the areas of similar rectangles are 8 cm² and 32 cm².



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