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.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.