Mathematics: Look at picture. Does anybody know the answer I’m lost?

Two equivalent expressions are 4 (6m+3)and 24m+12...

Look at picture. Does anybody know the answer I’m

andrewmena05

21.01.2022

Let x,y be the dimensions of the rectangle. We know the equations for both area and perimeter:

A=xy=36

$P=2(x+y)=36 \iff x+y=18$

So, we have the following system:

$\begin{cases}xy=36\\x+y=18\end{cases}$

From the second equation, we can deduce

y=18-x

Plug this in the first equation to get

xy=x(18-x)=-x^2+18=36

Refactor as

x^2-18x+36=0

And solve with the usual quadratic formula to get

$x=9\pm3\sqrt{5}$

Both solutions are feasible, because they're both positive.

If we chose the positive solution, we have

$x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}$

If we choose the negative solution, we have

$x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}$

So, we're just swapping the role of and . The two dimensions of the rectangle are $9+3\sqrt{5}$ and $9-3\sqrt{5}$

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