a rectangle and an equilateral triangle have the same perimeter the length of the rectangle is 4 times its width the length of each side of the triangle is 55 centimeters what is the length,in centimeter of the triangle

rectangle:

width -- x
length -- 4x
perimeter of rectangle = 2x + 8x = 10x

perimeter of triangle = 3(55) = 165

so 10x = 165
x = 16.5

then length of rectangle = 4x = 4(16.5) = 66

To solve this problem, we need to determine the length of the equilateral triangle when both the rectangle and the triangle have the same perimeter.

Let's start by finding the perimeter of the rectangle. We are given that the length of the rectangle is four times its width. Let's assume the width of the rectangle is represented by the variable "x." Therefore, the length of the rectangle would be 4x.

To find the perimeter of the rectangle, we add all four sides together. In this case, the perimeter of the rectangle is given to be equal to the perimeter of the triangle, so we can set up an equation:

Perimeter of Rectangle = Perimeter of Triangle

2(length + width) = 3 * side length (since an equilateral triangle has three equal sides)

Substituting the values, we have:

2(4x + x) = 3 * 55

Simplifying the equation:

2(5x) = 165

10x = 165

Dividing both sides by 10:

x = 16.5

Now that we know the width of the rectangle is 16.5 centimeters, we can find the length by multiplying it by 4:

Length of Rectangle = 4 * 16.5 = 66 centimeters

Since the triangle has three equal sides, each side length is given as 55 centimeters.

Therefore, the length of the equilateral triangle is 55 centimeters.