Question

In a parallelogram, two adjacent sides are 2.c – 7 and 3x – 6. If the perimeter of the parallelogram is 34, find x and the shorter side of the parallelogram X= Shorter Side =

Answer 1

Given the information on the problem, we have the following parallelogram:

since the perimeter is 34, we can write the following equation:

`2(3x-6)+2(2x-7)=34`

solving for x, we get:

`\begin{gathered} 2(3x-6)+2(2x-7)=34 \\ \Rightarrow6x-12+4x-14=34 \\ \Rightarrow10x-26=34 \\ \Rightarrow10x=34+26=60 \\ \Rightarrow x=(60)/(10)=6 \\ x=6 \end{gathered}`

now that we have that x = 6, we can find the measure of the sides:

`\begin{gathered} x=6 \\ 3(6)-6=18-6=12 \\ 2(6)-7=12-7=5 \end{gathered}`

therefore, x = 6 and the shorter side measures 5 units