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

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