Question

quadrilateral a has side lengths 3, 6, 6, and 9. quadrilateral b is a scaled copy of a with a shortest side length equal to 2. jada says, \since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total.\ complete the statement about whether you agree with jada. select choice with jada because the perimeter goes down by select choice units. (lesson 1 - 3)

Explanation:

Step1: Calculate the perimeter of quadrilateral A

The side - lengths of quadrilateral A are 3, 6, 6, and 9. The perimeter of quadrilateral A, $P_A=3 + 6+6 + 9=24$.

Step2: Find the scale factor

The shortest side of quadrilateral A is 3, and the shortest side of quadrilateral B is 2. The scale factor $k=\frac{2}{3}$.

Step3: Calculate the side - lengths of quadrilateral B

The side - lengths of quadrilateral B are $3\times\frac{2}{3}=2$, $6\times\frac{2}{3}=4$, $6\times\frac{2}{3}=4$, and $9\times\frac{2}{3}=6$.

Step4: Calculate the perimeter of quadrilateral B

The perimeter of quadrilateral B, $P_B=2 + 4+4 + 6=16$.

Step5: Calculate the difference in perimeters

The difference in perimeters $\Delta P=P_A - P_B=24 - 16 = 8$.

Answer:

Disagree; 8