Question

2. Given that the quadrilateral PQRS is a parallelogram, ST = 6x + 3 andQT= 4x + 27, what is the length of QS?161145138150None of these answers are correct

Answer 1

Given: The quadrilateral PQRS

To Determine: The value of QS

Solution

Please note that the diagonal of a quadrilaterals bisect each other. This is as shown below

Therefore ST equals QT

$\begin{gathered} ST=QT \\ 6x+3=4x+27 \\ 6x-4x=27-3 \\ 2x=24 \\ x=\frac{24}{2} \\ x=12 \end{gathered}$$\begin{gathered} QS=ST+QT \\ QS=6x+3+4x+27 \\ QS=10x+30 \\ QS=10(12)+30 \\ QS=120+30 \\ QS=150 \end{gathered}$

Hence QS = 150