An equilateral triangle and a square both have perimeters of 48 inches. What is the ratio of the length of the side of the triangle to the length of the side of the square? Express your answer as a common fraction.
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To find the ratio of the length of the side of the equilateral triangle to the length of the side of the square, we first need to determine the length of each side.
Let's start with the square. The perimeter of a square is given by four times the length of its side. Since the perimeter is 48 inches, we can divide it by 4 to find the length of one side:
48 inches ÷ 4 = 12 inches
So, the length of one side of the square is 12 inches.
Next, let's find the length of the side of the equilateral triangle. An equilateral triangle has three equal sides, so the perimeter is three times the length of one side. Since the perimeter is also 48 inches, we can divide it by 3 to find the length of one side:
48 inches ÷ 3 = 16 inches
Therefore, the length of one side of the equilateral triangle is 16 inches.
To find the ratio of the length of the side of the triangle to the length of the side of the square, we divide the length of the triangle's side by the length of the square's side:
16 inches ÷ 12 inches = 4/3
Therefore, the ratio of the length of the side of the equilateral triangle to the length of the side of the square is 4/3.