Question

Help me with math and explain it in a short solution

Answer 1

The perimeter is the sum of all the sides of a geometric figure. Since it is a parallelogram, then its opposite sides are equal, so

`\begin{gathered} QR=TS \\ \text{and} \\ QT=RS \end{gathered}`

In the graph, we can see that the distance between points Q and R is 7 units. To find the distance between points Q and T we can use the formula of the distance between two points in the plane, that is,

`\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Where} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are the coordinates of the points } \end{gathered}`

Then, we have

`\begin{gathered} Q(-3,3) \\ T(-5,-3) \\ d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ Replace} \\ d=\sqrt[]{(-5-(-3))^2+(-3-3)^2} \\ d=\sqrt[]{(-5+3)^2+(-3-3)^2} \\ d=\sqrt[]{(-2)^2+(-6)^2} \\ d=\sqrt[]{4+36} \\ d=\sqrt[]{40} \end{gathered}`

Finally, we have

`\begin{gathered} \text{ Perimeter }=QR+RS+TS+QT \\ \text{ Perimeter }=7+\sqrt[]{40}+7+\sqrt[]{40} \\ \text{ Perimeter }=26.65 \end{gathered}`

Therefore, the perimeter of parallelogram QRST is 26.65 units and the correct answer is option B.