Question

solve each exercise. mr. bailey can join a country club that would allow him to play a round of golf. how many hours the membership, the country club charges $55 for each round of golf. mr. bailey have to play for the cost to be the same with and without a membership? 10. find the value of x so that each pair of polygons has the same perimeter. then solve.

Explanation:

Step1: Find the perimeter of the hexagon

The hexagon has 6 sides each of length $5x$. So the perimeter $P_{hexagon}=6\times5x = 30x$.

Step2: Find the perimeter of the triangle

The sides of the triangle are $x + 14$, $8x+9$ and $x + 17$. So the perimeter $P_{triangle}=(x + 14)+(8x + 9)+(x + 17)=10x+40$.

Step3: Set the perimeters equal

Since the perimeters of the two polygons are the same, we set up the equation $30x=10x + 40$.

Step4: Solve the equation for x

Subtract $10x$ from both sides: $30x-10x=10x + 40-10x$, which gives $20x=40$. Then divide both sides by 20: $x=\frac{40}{20}=2$.

Answer:

$x = 2$