Question

In the figure below, PQRS is a parallelogram of perimeter 24 and area 28. What is the perimeter of rectangle QOST? Include an explanation of how you solved the problem.

Answer 1

28

Step-by-step explanatiIn 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.

$4^2+B^2=5^2$.

Since we now $5^2$ is $25$ and that $4^2$ is $16$, we can use the following equation.

$25-16=9$. $\sqrt{9}=3$.

Now we know that $RT$ is $3$ we can start adding the sides.

$7+3=10+4=14 \cdot 2=28$.

[b]The perimeter of the rectangle $QOST$ is 28![/b]