The side of a square is 4cm longer than the side of an equilateral triangle. The perimeter of the square is 28cm longer than the perimeter of the triangle. Find the length of the sides of the triangle and the sides of the square.

side of triangle -- x

perimeter of triangle = 3x

side of square = x+4
perimeter of square = 4(x+4) = 4x + 16

4x+16 - 3x = 28
x = 12

State conclusions

side of square=16

side of triangle=12

Sure, let's solve this math puzzle with a touch of humor!

Let's start by calling the side length of the equilateral triangle "x" cm. Therefore, the side length of the square will be "x + 4" cm, since it's 4 cm longer than the triangle.

Now, the formula for the perimeter of an equilateral triangle is simply three times the side length. So the perimeter of the triangle is 3x cm.

On the other hand, the perimeter of the square is four times the side length. Hence, the perimeter of the square is 4(x+4) cm.

According to our problem, the perimeter of the square is 28 cm longer than the perimeter of the triangle. So, we can set up the equation:

4(x+4) = 3x + 28

Now, let's solve this equation, step by step!

4x + 16 = 3x + 28

Subtracting 3x from both sides:

4x - 3x + 16 = 28

Simplifying:

x + 16 = 28

Subtracting 16 from both sides:

x = 28 - 16

x = 12

So, the side length of the equilateral triangle is 12 cm.

Now, we can find the side length of the square by using the equation "x + 4":

12 + 4 = 16

Therefore, the side length of the square is 16 cm.

To recap:
- The side length of the triangle is 12 cm.
- The side length of the square is 16 cm.

I hope this answer squared away any doubts you had about the lengths!

Let's assume the side length of the equilateral triangle is x cm.

The side length of the square is 4 cm longer than the side length of the triangle, so it is (x + 4) cm.

The perimeter of the equilateral triangle is three times the length of one side, so it is 3x cm.

The perimeter of the square is four times the length of one side, so it is 4(x + 4) cm.

According to the given information, the perimeter of the square is 28 cm longer than the perimeter of the triangle, so we can set up the following equation:

4(x + 4) = 3x + 28

Simplifying the equation:

4x + 16 = 3x + 28

Subtracting 3x from both sides:

x + 16 = 28

Subtracting 16 from both sides:

x = 12

Therefore, the side length of the equilateral triangle is 12 cm.

The side length of the square is (x + 4) cm = (12 + 4) cm = 16 cm.

So, the length of the sides of the triangle is 12 cm, and the length of the sides of the square is 16 cm.

To solve this problem, let's denote the side of the equilateral triangle as "x" cm.

According to the given information, the side of the square is 4 cm longer than the side of the equilateral triangle. Therefore, the side length of the square can be expressed as "x + 4" cm.

Additionally, the perimeter of an equilateral triangle is found by multiplying the length of one side by 3, while the perimeter of a square is found by multiplying the length of one side by 4.

Now, we can set up two equations based on the given information:

Equation 1: Perimeter of the square = Perimeter of the triangle + 28cm
4(x + 4) = 3x + 28

Equation 2: Side length of the square = Side length of the triangle + 4cm
x + 4 = x + 4

Now, let's solve Equation 1 for x:

4x + 16 = 3x + 28
4x - 3x = 28 - 16
x = 12

Substituting the value of x into Equation 2, we can find the side length of the square:

Side length of the square = 12 + 4
Side length of the square = 16 cm

Therefore, the side length of the equilateral triangle is 12 cm, and the side length of the square is 16 cm.