A Square shaped animal pen and a pen shaped like an equilateral triangle have an equal perimeters. Find the length of the sides of each pen if the sides of the triangular pen are 16 less than twice a side of the square

Pen.

Let's assume that the side length of the square animal pen is "s".

Therefore, each side of the equilateral triangular pen is equal to "2s - 16", as it is 16 less than twice the side length of the square pen.

The perimeter of the square pen is given by the formula:
Perimeter of square = 4 * side length

Therefore, the perimeter of the square pen is:
Perimeter of square = 4s

The perimeter of the equilateral triangular pen is given by the formula:
Perimeter of triangle = 3 * side length

Therefore, the perimeter of the triangular pen is:
Perimeter of triangle = 3 * (2s - 16)

Since we are given that the perimeters of both pens are equal, we can equate the two expressions for the perimeters:

4s = 3 * (2s - 16)

Now let's solve this equation for "s".

Multiplying out the equation:
4s = 6s - 48

Rearranging the equation:
2s = 48

Dividing both sides by 2:
s = 24

The side length of the square pen is 24 units.

Now we can find the side length of the triangular pen:
Side length of triangle = 2s - 16 = 2 * 24 - 16 = 48 - 16 = 32

Therefore, the side length of the triangular pen is 32 units.

To solve this problem, let's first assign variables to the unknown values.

Let's call the side length of the square pen "s" and the side length of the triangular pen "t".

Since we are given that the sides of the triangular pen are 16 less than twice a side of the square pen, we can write the equation:

t = 2s - 16

We are also given that the perimeter of the square pen is equal to the perimeter of the triangular pen.

The perimeter of a square is given by the formula:
Perimeter = 4 * side length

So, the perimeter of the square pen is 4s.

The perimeter of an equilateral triangle is given by the formula:
Perimeter = 3 * side length

So, the perimeter of the triangular pen is 3t.

Since the perimeters are equal, we can set up the equation:

4s = 3t

Now, let's substitute the value of t from the first equation into the second equation:

4s = 3(2s - 16)

Simplifying the equation:

4s = 6s - 48

Rearranging the equation:

2s = 48

Dividing both sides by 2:

s = 24

Now that we have found the value of s (the side length of the square pen), we can substitute it back into the first equation to find the value of t (the side length of the triangular pen):

t = 2 * 24 - 16
t = 32

Therefore, the length of the sides of the square pen is 24, and the length of the sides of the triangular pen is 32.

Just translate the English into Math

"the length of the sides of each pen if the sides of the triangular pen are 16 less than twice a side of the square
Pen."
if side of square is x
side of triangular pen is 2x-16

perimeter of square --- 4x
perimeter of triangle -- 3(2x-16) = ..

aren't they supposed to be equal ??
so .....

take over.