Respuesta :
Answer:
Width of rectangular storage room= 5 feet.
Step-by-step explanation:
Let x be the width of storage room.
We have been given that the length of a rectangular storage room is 3 feet longer than its width. So the length of storage room will be x+3.
We are also given that the area of the room is 40 square feet.
Since the area of a rectangle is length times width.
[tex]\text{Area of rectangle}=\text{Length* Width}[/tex]
Let us substitute our given values in area formula.
[tex]40=x*(x+3)[/tex]
Upon distributing x we will get,
[tex]40=x^2+3x[/tex]
[tex]x^2+3x-40=0[/tex]
Now let us factor out our quadratic equation using splitting the middle term.
[tex]x^2+8x-5x-40=0[/tex]
[tex]x(x+8)-5(x+8)=0[/tex]
[tex](x+8)(x-5)=0[/tex]
[tex]x+8=0[/tex] or [tex]x-5=0[/tex]
[tex]x=-8[/tex] or [tex]x=5[/tex]
Since width can not be negative, therefore, the width of rectangle will be 5 feet.
Let us verify our answer.
Length of rectangular storage room is 3 feet longer than its width. So length will be 5+3=8.
Given: Area=40 square feet.
5*8=40.
Hence, width of rectangular storage room is 5 feet.
