Question

A. Find the value of x and y that would make the quadrilateral STUV a paralelogram.B. Find the perimeter of STUV.

Answer 1

For the given quadrilateral to be a parallelogram, opposite sides must be congruent.

Therefore,

`\begin{gathered} 24-x=x+6 \\ 24-6=x+x \\ 18=2x \\ x=9 \end{gathered}`
`x+6=9+6=15`

Also, we have that:

`\begin{gathered} y=2x+3 \\ \text{ Since }y=9\text{ it follows that:} \\ y=2(9)+3=18+3=21 \end{gathered}`

Therefore, y = 21 and x = 9

Hence, the perimeter is given by:

`2(15+21)=72\text{ units}`

Therefore, the values of x and y are y = 21 and x = 9.

The perimeter is 72 units