The distance between goalpost, BC, is three times the distance from the top of the goalpost to the bottom. If the perimeter of ABCD is 21 1/3 yards, what is the length of BC

Let's denote the distance from the top to the bottom of the goalpost as x.

According to the problem, the distance between the goalposts, BC, is three times x, so BC = 3x.

The perimeter of ABCD is equal to the sum of all four sides, which is given as 21 1/3 yards.

The perimeter can be expressed as:

Perimeter = AB + BC + CD + DA

Since AB = CD (both are vertical sides), we can rewrite the perimeter equation as:

Perimeter = AB + BC + AB + DA

Given that AB + BC + AB + DA = 21 1/3 yards, we can simplify it as:

2(AB + BC + DA) = 21 1/3 yards

Now, let's substitute BC with 3x:

2(AB + 3x + DA) = 21 1/3 yards

Next, we need more information or equations to solve for the lengths of AB and DA, or their relationship to x.

Can you provide any additional information or equations?

To find the length of BC, we need to first set up an equation based on the given information.

Let's assume the distance from the top of the goalpost to the bottom is "x" yards. Based on the problem statement, we know that the distance between the goalposts, BC, is three times the distance from the top to the bottom. So, BC = 3x.

The perimeter of the shape ABCD is given as 21 1/3 yards. Perimeter is the sum of all the sides of the shape.

The shape ABCD has four sides: AB, BC, CD, and AD. Since AB and CD are the same length (goalposts are parallel), we can say that AB + BC + CD + AD = Perimeter.

Let's substitute the values we have into this equation:
AB + BC + CD + AD = 21 1/3

Since AB is parallel to CD, they have the same length. Let's call this length "y". We now have:
2y + BC + BC = 21 1/3

Since BC = 3x, we can substitute this into the equation:
2y + 3x + 3x = 21 1/3

Simplifying the equation:
2y + 6x = 21 1/3

Now, we need one more piece of information to solve for x. If we know the relationship between the length of AB/CD and BC, we can solve the equation. Could you provide that information?

height of goalpost = x

width of goalpost = 3x

2(x+3x) = 21 1/3
8x = 64/3
x = 8/3

65