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Lapatulllka [165]
3 years ago
5

Find the dimensions of a rectangle whose area is 285 cm2 and whose perimeter is 68 cm.

Mathematics
1 answer:
enyata [817]3 years ago
7 0
\bf \textit{area of a rectangle}\\\\
A=lw\quad 
\begin{cases}
l=length\\
w=width\\
-----\\
A=285
\end{cases}\implies 285=lw\implies \boxed{\cfrac{285}{w}=l}
\\\\\\
\textit{perimeter of a rectangle}\\\\
P=2(l+w)\quad 
\begin{cases}
l=\frac{285}{w}\\\\
P=68
\end{cases}\implies 68=2\left( \boxed{\cfrac{285}{w}}+w \right)
\\\\\\
\cfrac{68}{2}=\cfrac{285}{w}+w\implies 34=\cfrac{285+w^2}{w}\implies 34w=285+w^2

\bf 0=w^2-34w+285\implies 0=(w-19)(w-15)\implies w=
\begin{cases}
19\\
15
\end{cases}
\\\\\\
\stackrel{lenght}{l}=
\begin{cases}
\frac{285}{19}\implies &15\\\\
\frac{285}{15}\implies &19
\end{cases}
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