5. kyle puts ribbon around his rectangular bulletin board, which measures $$ 24 \frac{3}{4} $$ inches by $$ 36 \frac{5}{8} $$ inches. How much ribbon does he need?

Question

UpStudy AI · Accepted Answer

To determine how much ribbon Kyle needs to put around his rectangular bulletin board, we need to calculate the perimeter of the rectangle. The perimeter $$ P $$ of a rectangle is given by the formula:

$$
P = 2 \times (\text{length} + \text{width})
$$

**Given Dimensions:**
- Length = $$ 36 \frac{5}{8} $$ inches
- Width = $$ 24 \frac{3}{4} $$ inches

**Step 1: Convert Mixed Numbers to Improper Fractions**

Convert both measurements to improper fractions for easier calculation.

$$
36 \frac{5}{8} = \frac{36 \times 8 + 5}{8} = \frac{288 + 5}{8} = \frac{293}{8}
$$

$$
24 \frac{3}{4} = \frac{24 \times 4 + 3}{4} = \frac{96 + 3}{4} = \frac{99}{4}
$$

**Step 2: Find a Common Denominator and Add**

To add these two fractions, they need to have the same denominator. The least common denominator (LCD) of 8 and 4 is 8.

$$
\frac{99}{4} = \frac{99 \times 2}{4 \times 2} = \frac{198}{8}
$$

Now, add the two fractions:

$$
\frac{198}{8} + \frac{293}{8} = \frac{198 + 293}{8} = \frac{491}{8}
$$

**Step 3: Calculate the Perimeter**

Multiply the sum by 2 to find the perimeter:

$$
P = 2 \times \frac{491}{8} = \frac{982}{8} = \frac{491}{4}
$$

Convert the improper fraction back to a mixed number:

$$
\frac{491}{4} = 122 \frac{3}{4} \text{ inches}
$$

**Conclusion:**

Kyle needs **$$ 122 \frac{3}{4} $$ inches** of ribbon to wrap around his bulletin board.

**Answer:**  
Kyle needs $$122\, \frac{3}{4}$$ inches of ribbon.
Kyle needs $$122 \frac{3}{4}$$ inches of ribbon.

kyle puts ribbon around his rectangular
bulletin board, which measures inches
by inches. How much ribbon does
he need?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Geometry Questions

kyle puts ribbon around his rectangular bulletin board, which measures inches by inches. How much ribbon does he need?