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I need help figuring out how to solve the length

I need help figuring out how to solve the length-example-1

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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

User Cassandre
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