 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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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