Question

The perimeter of the pentagon below is 56 units. Find the value of x.

Answer 1

Given:

The perimeter of the pentagon, P=56 units.

From the figure, the sides of the pentagon are 2x, 10, x+2, 3x-2 and 10.

The sum of sides of the pentagon is equal to its perimeter.

Hence, the perimeter can be expressed as,

`\begin{gathered} P=2x+x+2+3x-2+10+10 \\ P=6x+20 \end{gathered}`

Now, put P=56 in the above equation and solve for x.

`\begin{gathered} 56=6x+20 \\ 56-20=6x \\ 36=6x \\ (36)/(6)=x \\ 6=x \end{gathered}`

Therefore, the value of x is 6.