casey’s den is 10feet longer than it is wide. If the​ den’s area is 119 square​ feet, what are the dimensions of the​ room?

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casey’s den is 10feet longer than it is wide. If the​ den’s area is 119 square​ feet, what are the dimensions of the​ room?

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Eirian 3 years 2021-08-14T16:00:10+00:00 1 Answers 7 views 0

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    2021-08-14T16:01:37+00:00

    Answer:

    The width is 7ft and the length is 17 ft

    Step-by-step explanation:

    Let w represent the width of the room and L represents the length of the den.

    Given that:

    caseys den is 10feet longer than it is wide

    Then;

    w + 10 = L —- (1)

    The area of the den = 119 ft²

    Area = w × L

    119 = w × L  —- (2)

    From equation (1);

    let w = L – 10.

    Now we can replace the value of w into equation (2)

    i.e.

    (L – 10) × L = 119

    L² – 10L – 119 = 0

    (L + 7) ( L – 17) = 0

    L + 7 = 0 or L – 17 = 0

    L = – 7 ft  or L = 17 ft

    Recall that:

    w = L – 10

    w = -7 – 10    or    w = 17 – 10

    w = -17         or     w = 7 ft

    The area of the den can now be:

    Area = -17 ft × – 7ft   or       17ft ×  7 ft

    Area = 119 ft²           or        119 ft²

    Since it is ideal to use the positive integer,

    Then the width is 7ft and the length is 17 ft

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