Question

quadrilateral a has side lengths 6, 9, 9, and 12. quadrilateral b is a scaled copy of quadrilateral a, with its shortest side of length 2. what is the perimeter of quadrilateral b?

Explanation:

Step1: Determine the scale factor

The shortest side of Quadrilateral A is 6, and the shortest side of Quadrilateral B (the scaled copy) is 2. The scale factor \( k \) is the ratio of the corresponding sides, so \( k=\frac{2}{6}=\frac{1}{3} \).

Step2: Find the perimeter of Quadrilateral A

First, calculate the perimeter of Quadrilateral A. The side lengths are 6, 9, 9, and 12. So the perimeter \( P_A = 6 + 9 + 9 + 12 \).
\( P_A=6 + 9+9 + 12=36 \).

Step3: Calculate the perimeter of Quadrilateral B

When a figure is scaled by a factor \( k \), its perimeter is also scaled by \( k \). So the perimeter of Quadrilateral B \( P_B=k\times P_A \).
Substitute \( k = \frac{1}{3} \) and \( P_A = 36 \) into the formula: \( P_B=\frac{1}{3}\times36 = 12 \).

Answer:

The perimeter of Quadrilateral B is 12.