To determine which measures are true for the quilt piece, let's analyze the relevant information step-by-step:
1. Side Length Calculation:
The perimeter of the rhombus is given as 16 inches. Since a rhombus has four equal sides, we can determine the length of each side by dividing the perimeter by the number of sides:
[tex]\[
\text{Side length} = \frac{16 \text{ inches}}{4} = 4 \text{ inches}
\][/tex]
2. Longer Diagonal Calculation:
We're given that one of the diagonals equals the side length of the rhombus. However, we also know that the length of the longer diagonal is approximately 7 inches. This value is given as true.
3. Greater Interior Angle Calculation:
In the context of this problem, the measure of the greater interior angle of the rhombus is specified to be 90 degrees.
Given these analyses, the correct measurements for the quilt piece include:
- The perimeter of the rhombus is 16 inches.
- The measure of the greater interior angle of the rhombus is 90 degrees.
- The length of the longer diagonal is approximately 7 inches.
Therefore, the three true measurements are:
1. The perimeter of the rhombus is 16 inches.
2. The measure of the greater interior angle of the rhombus is 90 degrees.
3. The length of the longer diagonal is approximately 7 inches.
