Mathematics

Question

The area of a rectangular room is 750 square feet. the width of the room is 5 feet less than the length of the room. which equations can be used to solve for y, the length of the room?

2 Answer

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  • Answer:

    Width=25 ft and length=30 ft

    Step-by-step explanation:

    In order to find the answer let's remember that the area (A) of a rectangle is:

    [tex]A=width*length[/tex]

    Let's assume that the length of the room is 'X' feet.

    Becuase the problem mentioned that the width (Y) of the room is 5 feet less than the length, then:

    [tex]Y=X-5[/tex]

    Now, using the area equation we have:

    A=width*length

    [tex]750=X*Y[/tex] but using the width expression we have:

    [tex]750=X*(X-5)[/tex]

    [tex]0=X^2-5X-750[/tex]

    Using the root's equation we have:

    [tex]X=\frac{-b\±\sqrt{b^{2}-4ac}}{2a}[/tex]

    [tex]X=\frac{-(-5)\±\sqrt{(-5)^{2}-(4*1*(-750)}}{2*1}[/tex]

    [tex]X1=30[/tex]

    [tex]X1=-25[/tex]

    Because the length (X) can't be negative, then length=30 feet. In order to find the width we have:

    [tex]Y=X-5[/tex]

    [tex]Y=30-5[/tex]

    [tex]Y=25[/tex]

    So the width is 25 feet.

    In conclusion the room has a width=25 ft and length=30 ft.

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