Question

from unit 1, lesson 3. 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.\ do you agree with jada? explain your reasoning.

Explanation:

Step1: Find the scale - factor

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

Step2: Find the new side - lengths of quadrilateral B

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

Step3: Calculate the perimeters of A and B

The perimeter of quadrilateral A, $P_A=3 + 6+6 + 9=24$. The perimeter of quadrilateral B, $P_B=2 + 4+4 + 6=16$.

Step4: Analyze Jada's statement

The difference in perimeters is $P_A - P_B=24 - 16 = 8$, not 4. So Jada is wrong.

Answer:

No, Jada is incorrect. The side - lengths are scaled by a factor of $\frac{2}{3}$, not decreased by 1 each. The perimeter of quadrilateral A is 24 and the perimeter of quadrilateral B is 16, so the perimeter decreases by 8, not 4.