Question
Quadrilateral a has side length six, nine, nine, and 12. Quadrilateral B is a scaled copy of quadrilateral a, with its shortest side of length too. What is the perimeter of quadrilateral b?
Answers
GPT-4o mini
To solve for the perimeter of quadrilateral B, we start by determining the perimeter of quadrilateral A, which has side lengths of 6, 9, 9, and 12.
First, we calculate the perimeter of quadrilateral A:
\[
\text{Perimeter of A} = 6 + 9 + 9 + 12 = 36
\]
Quadrilateral B is a scaled copy of quadrilateral A, and its shortest side has been defined as 2. The shortest side of quadrilateral A is 6. We find the scale factor between quadrilateral A and quadrilateral B:
\[
\text{Scale factor} = \frac{\text{length of shortest side of B}}{\text{length of shortest side of A}} = \frac{2}{6} = \frac{1}{3}
\]
Next, we use this scale factor to find the perimeter of quadrilateral B:
\[
\text{Perimeter of B} = \text{Perimeter of A} \times \text{Scale factor} = 36 \times \frac{1}{3} = 12
\]
Therefore, the perimeter of quadrilateral B is
\[
\boxed{12}
\]
First, we calculate the perimeter of quadrilateral A:
\[
\text{Perimeter of A} = 6 + 9 + 9 + 12 = 36
\]
Quadrilateral B is a scaled copy of quadrilateral A, and its shortest side has been defined as 2. The shortest side of quadrilateral A is 6. We find the scale factor between quadrilateral A and quadrilateral B:
\[
\text{Scale factor} = \frac{\text{length of shortest side of B}}{\text{length of shortest side of A}} = \frac{2}{6} = \frac{1}{3}
\]
Next, we use this scale factor to find the perimeter of quadrilateral B:
\[
\text{Perimeter of B} = \text{Perimeter of A} \times \text{Scale factor} = 36 \times \frac{1}{3} = 12
\]
Therefore, the perimeter of quadrilateral B is
\[
\boxed{12}
\]