Question

I need help figuring out how to solve the length

Answer 1

We have the parallel sides of the rectangle are equal, therefore:

`\begin{gathered} RS=QP=4x+3 \\ \text{and} \\ SP=RQ=5x \end{gathered}`

The perimeter is the sum of all sides, then:

`RS+QP+SP+RQ=222`

Substitute the given data:

`(4x+3)+(4x+3)+5x+5x=222`

And solve for x:

`\begin{gathered} 4x+3+4x+3+5x+5x=222 \\ 18x+6=222 \\ 18x+6-6=222-6 \\ 18x=216 \\ (18x)/(18)=(216)/(18) \\ x=12 \end{gathered}`

Next, we find the length of side RS:

`RS=4x+3=4(12)+3=48+3=51`

Answer: RS = 51 units