The perimeter of a rectangle with one side four times the other is equal to the perimeter

| May 24, 2021 | education

The perimeter of a rectangle with one side four times the other is equal to the perimeter of the rhombus with side 15. Find the sides of the rectangle. In your answer, indicate the length of the longer side.

The perimeter of a rhombus is equal to the sum of the lengths of its four sides. Since all sides are equal in a rhombus, we find its perimeter by the formula P = 4a.

P = 4 * 15 = 60.

Let the length of one side of the rectangle be x, then the length of the second side of the rectangle is 4x. By the condition of the problem, it is known that the perimeter of the rectangle (the perimeter of the rectangle is equal to the sum of the lengths of its sides; P = 2 (a + b)) is equal to 2 (x + 4x) or 60. Let’s make an equation and solve it.

2 (x + 4x) = 60;

2 * 5x = 60;

10x = 60;

x = 60: 10;

x = 6 – first side;

4x = 6 * 4 = 24 – the second, large side.

Answer. 24.



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