Question

Solve the problems. A regular pentagon and an equilateral triangle have the same perimeter. The perimeter of the pentagon is 5 (3x + 2) inches. The perimeter of the triangle is 4 (x - 2) inches. What is the perimeter of each figure? A 12 inches B 20 inches C 36 inches D 40 inches

Answer 1

`5((1)/(2)x+2)`
`4(x-2)`

Start by finding the value of x by making both expressions equal

`5\cdot((1)/(2)x+2)=4(x-2)`

distribut 5 and 4 on their corresponding sides

`\begin{gathered} (5)/(2)x+10=4x-8 \\ \end{gathered}`

let all xs' to one side and all constants to the other

`\begin{gathered} (5)/(2)x-4x=-8-10 \\ (-3)/(2)x=-18 \end{gathered}`

solve x by dividing by -3 and multiplying by 2

`\begin{gathered} x=-18\cdot((2)/(-3)) \\ x=12 \end{gathered}`

after finding the value of x into either one of the equations

`4(x-2)`
`\begin{gathered} 4\cdot(12-2) \\ 4\cdot10 \\ 40 \end{gathered}`

the perimeter of each figure is 40 inches.