Question

quadrilateral a has side lengths 3, 6, 6, and 9. quadrilateral b is a scaled copy of a with the 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.\ do you agree with jada? a no. the side lengths of quadrilateral b are $\frac{2}{3}$ of those of quadrilateral a. this means bs side lengths are 2, 4, 4, and 6. the perimeter of a is 24 and the perimeter of b is 16, so it decreased by 8. b no. the side lengths of quadrilateral b are $\frac{3}{2}$ of those of quadrilateral a. this means bs side lengths are 2, 4, 4, and 6. the perimeter of a is 24 and the perimeter of b is 16, so it decreased by 8. c yes. jadas reasoning is correct. the perimeter of quadrilateral a is 24. the side lengths of quadrilateral b are 2, 5, 5, and 8, which makes the perimeter 20 and that is 4 less than 24. d no. the side lengths of quadrilateral b are $\frac{1}{3}$ of those of quadrilateral a. this means bs side lengths are 1, 2, 2, and 3. the perimeter of a is 24 and the perimeter of b is 18, so it decreased by 16

Explanation:

Step1: Calculate the perimeter of Quadrilateral A

The side - lengths of Quadrilateral A are 3, 6, 6, and 9. The perimeter of 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

Multiply the side - lengths of Quadrilateral A by the scale factor. The side - lengths of 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 B, $P_B=2 + 4+4 + 6=16$.

Step5: Calculate the difference in perimeters

The difference in perimeters is $P_A - P_B=24−16 = 8$. So Jada is wrong.

Answer:

A. No. The side lengths of Quadrilateral B are $\frac{2}{3}$ of those of Quadrilateral A. This means Bs side lengths are 2, 4, 4, and 6. The perimeter of A is 24 and the perimeter of B is 16, so it decreased by 8.