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1 June, 14:32

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. 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 equation can be used to solve for y, the length of the room? Check all that apply. a) y (y + 5) = 750b) y^2 - 5y = 750c) 750 - y (y - 5) = 0d) y (y - 5) + 750 = 0e) (y + 25) (y - 30) = 0

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  1. 1 June, 17:25
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    The correct options are

    (b) y²-5y=750

    (c) 750-y (y-5) = 0

    (e) (y+25) (y-30) = 0

    Step-by-step explanation:

    Given that,

    The area of rectangular room is 750 square feet.

    Let the length of the rectangular room be y feet.

    Since the width of the rectangular 5 less than the length of the room.

    Then the width of the given rectangular room is (y-5) feet.

    We know the area of a rectangular plot is = Length*width.

    The area of the rectangular room is = y (y-5) square feet

    According to problem,

    y (y-5) = 750 ... (1)

    ⇒y²-5y=750 ... (2)

    ⇒y²-5y-750=0

    ⇒y²-30y+25y-750=0

    ⇒y (y-30) + 25 (y-30) = 0

    ⇒ (y-30) (y+25) = 0 ... (3)

    ⇒y-30=0 or, y+25=0

    ⇒y = 30, - 25

    The length of a rectangle can't negative.

    So, x=30.

    We can rewrite the equation (1) in form of

    (i)

    y (y-5) = 750

    ⇒750 = y (y-5)

    ⇒750-y (y-5) = 0 ... (4)

    (ii)

    y (y-5) = 750

    ⇒y (y-5) - 750=0 ... (5)

    The correct options are

    (b) y²-5y=750

    (c) 750-y (y-5) = 0

    (e) (y+25) (y-30) = 0
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