The perimeter of a rectangle with one side twice as large as the other equals the perimeter

| August 23, 2021 | education

The perimeter of a rectangle with one side twice as large as the other equals the perimeter of the 6-sided rhombus. Find the sides of the rectangle.

1) A rhombus is a parallelogram in which all sides are equal.

The perimeter of a rhombus is determined by the formula:

P = a + a + a + a = 4a, where a is the side of the rhombus.

We calculate the perimeter of the rhombus:

P = 4 * 6 = 24.

2) Let x be the width of a given rectangle, then 2x is its length.

The perimeter of a rectangle is equal to the sum of the lengths of all its sides and will be determined by:

P = x + 2x + x + 2x = 6x.

3) Since the perimeter of the rectangle is equal to the perimeter of the rhombus, we write:

24 = 6x.

4) Find the width of the rectangle:

x = 24: 6 = 4.

5) Calculate the length of the rectangle:

2 * 4 = 8.

Answer: 8 and 4.



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