A rectangular porch has dimensions of S(x+12) and (x+5) feet.

ediculeN 2021-08-14 Answered
A rectangular porch has dimensions of \(\displaystyle{S}{\left({x}+{12}\right)}\) and \(\displaystyle{\left({x}+{5}\right)}\) feet. If the area of the porch floor is 120 square feet, what are its length and width?

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Expert Answer

Brighton
Answered 2021-08-15 Author has 16781 answers
Step 1
Given: A rectangular porch has dimensions of \(\displaystyle{S}{\left({x}+{12}\right)}\) and \(\displaystyle{\left({x}+{5}\right)}\) feet. If the area of the porch floor is 120 square feet.
To find: length and width of rectangular porch.
Step 2
Solutions: Let the length of rectangular porch be \(\displaystyle{\left({x}+{12}\right)}\) feet.
width of rectangular porch be \(\displaystyle{\left({x}+{5}\right)}\) feet.
Area of rectangular porch \(\displaystyle={120}\) sq. feet.
Now according question,
Area of rectangular body is given by
\(\displaystyle\Rightarrow{A}{r}{e}{a}={l}\times{w}\).
\(\displaystyle\Rightarrow{120}={\left({x}+{12}\right)}{\left({x}+{5}\right)}\)
\(\displaystyle\Rightarrow{\left({x}+{12}\right)}{\left({x}+{5}\right)}={120}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}+{5}{x}+{12}{x}+{60}={120}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}+{5}{x}+{12}{x}={120}-{60}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}+{17}{x}={60}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}+{17}{x}-{60}={0}\)
Step 3
\(\displaystyle\Rightarrow{x}^{{{2}}}+{20}{x}-{3}{x}-{60}={0}\).
\(\displaystyle\Rightarrow{x}{\left({x}+{20}\right)}-{3}{\left({x}+{20}\right)}={0}\)
\(\displaystyle\Rightarrow{\left({x}+{20}\right)}{\left({x}-{3}\right)}={0}\)
\(\displaystyle\Rightarrow{x}=+{3},-{20}\)
We choose (+ue) value of 'x' i.e. 3
Length of Rectangular porch \(\displaystyle={\left({x}+{12}\right)}\) feet
\(\displaystyle={\left({3}+{12}\right)}\) feet
\(\displaystyle={15}\) feet
width of rectangular porch \(\displaystyle={\left({x}+{5}\right)}\) feet
\(\displaystyle={\left({5}+{3}\right)}\) feet
\(\displaystyle={8}\) feet
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