An equilateral triangle is one in which the three sides are of equal measures. Suppose a rectangle and an equilateral triangle have the same perimeter. The length of the rectangle is three times the width. Each side of the triangle is 8 centimeters. Find the length and the width of the rectangle.
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Let's use the following variables to represent the dimensions of the rectangle:
l: length of the rectangle
w: width of the rectangle
We know that the perimeter of the equilateral triangle is equal to the perimeter of the rectangle, so we can write:
3(8) = 2l + 2w
Simplifying this equation, we get:
24 = 2l + 2w
We also know that the length of the rectangle is three times the width, so we can write:
l = 3w
Substituting this into the previous equation, we get:
24 = 2(3w) + 2w
Simplifying this equation, we get:
24 = 8w
Dividing both sides by 8, we get:
w = 3
So the width of the rectangle is 3 cm.
Using the equation l = 3w, we can find the length of the rectangle:
l = 3(3) = 9
So the length of the rectangle is 9 cm.
Therefore, the length and width of the rectangle are 9 cm and 3 cm, respectively.