In the diagram below, PQRS is a parallelogram with a perimeter of 26 and an area of 28. What is the perimeter of rectangle OSTQ? Include an explanation of how you solved the problem.
In order to solve this problem we need to find out what $QR$ is.
We know that the perimeter of the parallelogram was given as $24$ and that two of the sides were given as $5$. $5+5=10$ $24-10=14/2=7$. Now we know that the base was $7$.
We can find the height by taking the area that they gave us and dividing that by $7$. We get $4$.
Since we now know that the height of the parallelogram is $4$ that means $OQ$ is also $4$.
Next we need to find what $RT$ is.
Since we now $5^2$ is $25$ and that $4^2$ is $16$, we can use the following equation.
Now we know that $RT$ is $3$ we can start adding the sides.
$7+3=10+4=14 \cdot 2=28$.