MHB Justin's Question about Rectangle in Facebook

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The discussion revolves around solving a geometry problem involving a rectangle where the length is three times the width. The original area is represented by the equation A = xy, with y defined as 3x. When each side of the rectangle is increased by 6, the new area becomes 156 more than the original area. Participants suggest setting up equations based on these parameters to find the dimensions of the new rectangle. The focus is on deriving and solving these equations to determine the values of x and y.
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Justin on Facebook writes:

hi.. I am new to geometry and my teacher gave me this equation and i have no idea how to solve it.. can u guys help me pls?

the length of a rectangle is three times as long as the width. If each side is increased by 6, the area of the new rectangle is 156 more than the area of the original rectangle. What are the dimensions of the new rectangle?
 
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Hi Justin, :)

Take the width of the rectangle as \(x\) and the length as \(y\). Then, \(y=3x\). The equation for the area of the rectangle being,

\[A=xy\]

Try to write an equation for the area of the new rectangle in terms of \(x,\,y\mbox{ and }A\). Notice that the new length is \(y+6\) and the width is \(x+6\). Then you can try to solve the three equations and find \(x\mbox{ and }y.\)
 

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