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?
if triangle has side t and square has side s, then
3t = 4s
t/s = 4/3
To find the ratio of the length of the side of the equilateral triangle to the length of the side of the square, we need to determine their respective side lengths.
Let's start with the square. The perimeter of a square is given by the equation P = 4s, where P is the perimeter and s is the length of one side. In this case, the perimeter is 48 inches. We can solve for s by rearranging the equation:
48 = 4s
s = 48 / 4
s = 12 inches
So, the length of one side of the square is 12 inches.
Now, let's move on to the equilateral triangle. The perimeter of an equilateral triangle is given by P = 3s, where P is the perimeter and s is the length of one side. In this case, the perimeter is also 48 inches. We can solve for s by rearranging the equation:
48 = 3s
s = 48 / 3
s = 16 inches
So, the length of one side of the equilateral triangle is 16 inches.
To find the ratio, we divide the length of the side of the triangle by the length of the side of the square:
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.
To find the ratio of the length of the side of the triangle to the length of the side of the square, we need to determine the lengths of their sides first.
Let's start with the equilateral triangle.
An equilateral triangle has all sides of equal length. Let's denote the length of each side of the triangle as "a".
The perimeter of an equilateral triangle is the sum of the lengths of all its sides. Since all sides of the triangle have the same length, the perimeter of the triangle is given by
Perimeter of triangle = 3a
In this case, the perimeter of the equilateral triangle is given as 48 inches. Therefore, we have the equation:
3a = 48
Now, let's solve this equation to find the value of "a":
Dividing both sides of the equation by 3, we get:
a = 16
So, the length of each side of the equilateral triangle is 16 inches.
Moving on to the square:
A square has all sides equal in length. Let's denote the length of each side of the square as "b".
The perimeter of a square is four times the length of its side. So, the perimeter of the square, given as 48 inches, is given by:
Perimeter of square = 4b
Using the given information, we have:
4b = 48
Solving for "b" by dividing both sides of the equation by 4, we get:
b = 12
Therefore, the length of each side of the square is 12 inches.
Finally, 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 (16 inches) by the length of the square's side (12 inches):
Ratio = Length of triangle's side / Length of square's side = 16 / 12 = 4/3
So, the ratio of the length of the side of the triangle to the length of the side of the square is 4/3.