Question

1. write an equation to find the value of x so that each pair of polygons has the same perimeter. then solve.

10.

Explanation:

Step1: Find perimeter of first polygon in 9

Sum the side - lengths of the triangle: $(x + 3)+(x + 6)+(x + 9)=3x+18$.

Step2: Find perimeter of second polygon in 9

Sum the side - lengths of the rectangle: $2(x + 1)+2(x + 4)=2x+2 + 2x+8=4x + 10$.

Step3: Set perimeters equal

Set $3x+18 = 4x + 10$.

Step4: Solve for x

Subtract $3x$ from both sides: $18=x + 10$. Then subtract 10 from both sides: $x=8$.

Step5: Find perimeter of first polygon in 10

Sum the side - lengths of the hexagon: $6\times5x = 30x$.

Step6: Find perimeter of second polygon in 10

Sum the side - lengths of the triangle: $(8x + 9)+(x + 17)+(x + 14)=10x+40$.

Step7: Set perimeters equal

Set $30x=10x + 40$.

Step8: Solve for x

Subtract $10x$ from both sides: $20x=40$. Then divide both sides by 20: $x = 2$.

Answer:

For problem 9: $x = 8$
For problem 10: $x = 2$