Write and solve an equation to answer the question.

The perimeter of the Puerto Rican flag is 150 inches. What are the dimensions of the flag?

Equation: [tex]\(\square\)[/tex]

[tex]\(P = 2x + 2y = 150\)[/tex]

[tex]\(x = \square \)[/tex]

[tex]\(y = \square\)[/tex]

Label the dimensions of the flag. Dimensions are in inches.



Answer :

To find the dimensions of the Puerto Rican flag given its perimeter, we start by recalling the formula for the perimeter of a rectangle:

[tex]\[ P = 2 \times (\text{length} + \text{width}) \][/tex]

We are given that the perimeter is 150 inches. Putting this into the formula, we get:

[tex]\[ 2 \times (\text{length} + \text{width}) = 150 \][/tex]

To simplify this equation, we divide both sides by 2:

[tex]\[ \text{length} + \text{width} = 75 \][/tex]

Now, we need to solve for the length and the width. Without any additional information regarding the specific ratio between the length and width, we can propose a simple assumption. A reasonable assumption is that the length and width are equal, making the flag a square.

Assuming the dimensions are equal, we get:

[tex]\[ \text{length} = \text{width} \][/tex]

Substituting this into our simplified equation, we get:

[tex]\[ \text{length} + \text{length} = 75 \][/tex]

This can be rewritten as:

[tex]\[ 2\text{length} = 75 \][/tex]

Dividing both sides by 2, we find:

[tex]\[ \text{length} = 37.5 \][/tex]

Since the dimensions are equal,

[tex]\[ \text{width} = 37.5 \][/tex]

So, the dimensions of the Puerto Rican flag are:

- Length: 37.5 inches
- Width: 37.5 inches

### Summary:

The equation we solved is:

[tex]\[ 2 \times (\text{length} + \text{width}) = 150 \][/tex]

[tex]\[ \text{length} + \text{width} = 75 \][/tex]

Labeling the dimensions:

Length = 37.5 inches

Width = 37.5 inches

Thus, the dimensions of the Puerto Rican flag are 37.5 inches by 37.5 inches.