Questions: A pendant has a 3/4 inch by 2/3 inch rectangular shape with a 1/2 inch gold border. What are the dimensions of the pendant, including the gold border? (Use the larger value for length and the smaller value for width.)

Solution Steps

To find the dimensions of the pendant including the gold border, we need to add the border width to both the length and the width of the pendant. Since the border is on all sides, we add twice the border width to each dimension.

The given dimensions of the pendant are:

• Length: \( \frac{3}{4} \) inches
• Width: \( \frac{2}{3} \) inches

The gold border width is:

• Border width: \( \frac{1}{2} \) inch

To find the dimensions of the pendant including the gold border, we add twice the border width to both the length and the width.

\[ \text{New Length} = \frac{3}{4} + 2 \times \frac{1}{2} = \frac{3}{4} + 1 = \frac{3}{4} + \frac{4}{4} = \frac{7}{4} = 1.75 \text{ inches} \]

\[ \text{New Width} = \frac{2}{3} + 2 \times \frac{1}{2} = \frac{2}{3} + 1 = \frac{2}{3} + \frac{3}{3} = \frac{5}{3} \approx 1.6667 \text{ inches} \]

Final Answer