Question

The sides of a parallelogram QRST are shown below. What are the perimeter and area? Show or explain how you got your answer.

Answer 1

Opposite sides of a parallelogram,

`\begin{gathered} QR=ST \\ 3y+8=y+22 \\ 3y-y=22-8 \\ 2y=14 \\ y=(14)/(2) \\ y=7 \end{gathered}`

Similarly, x can be obtained as,

`\begin{gathered} RS=TQ \\ x-9=-3x+11 \\ x+3x=11+9 \\ 4x=20 \\ x=(20)/(4) \\ x=5 \end{gathered}`
`\begin{gathered} Perimeter=(3y+8)+(x-9)+(y+22)+(-3x+11) \\ =\lbrack(3*7)+8\rbrack+(5-9)+(7+22)+\lbrack(-3*5)+11\rbrack \\ =\lbrack21+8\rbrack+(-4)+(29)+\lbrack-15+11\rbrack \\ =29-4+29-4 \\ =58-8 \\ =50 \end{gathered}`

Hence, the perimeter of the parallelogram is 50 units.