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Sagot :
Answer:
a) w^2+14w-1632 = 0
b) Length = 48 feet
Width = 34 feet
Explanations:
a) Let the floor of the one-story building be a rectangle. The formula to calculate the area of the floor is expressed as;
[tex]A=lw[/tex]where;
l is the length of the storey building
w is the width of the one-storey building
If the floor of a one-story building is 14 feet longer than it is wide(w), hence;
[tex]l=w+14[/tex]Substitute the length function into the area of the floor to have;
[tex]\begin{gathered} A=(w+14)w \\ A=w^2+14w \\ \end{gathered}[/tex]If the building has 1632 square feet of floor space, hence the area of the floor will be expressed as;
[tex]\begin{gathered} 1632=w^2+14w \\ \text{Swap} \\ w^2+14w=1632 \\ w^2+14w-1632=0 \end{gathered}[/tex]b) To get the length and width of the floor, we will factorize the quadratic expression to have;
[tex]\begin{gathered} w^2+14w-1632=0 \\ w^2+48w-34w-1632=0 \\ w(w+48)-34(w+48)=0 \\ (w-34)(w+48)=0 \\ w-34=0\text{ and w+48 = 0} \\ w=34\text{ and -48} \end{gathered}[/tex]Since the width cannot be negative, hence w = 34 feet.
Recall that A = lw, hence;
[tex]\begin{gathered} l=\frac{A}{w} \\ l=\frac{1632}{34} \\ l=48ft \end{gathered}[/tex]Hence the length and width of the floor are 48feet and 34 feet respectively.
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