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25 November, 05:20

Solve the following problems. Be sure to indicate if a solution is to be rejected based on the contextual situation.

1. The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 15 cm2, find the width.

2. The ratio of length to width in a rectangle is 2 ∶ 3. Find the length of the rectangle when the area is 150 in2.

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  1. 25 November, 08:42
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    1. 5/3 cm

    2. 10 in

    Step-by-step explanation:

    1. The length of a rectangle is 4 cm more than 3 times its width.

    Let the length be L and the width B

    Then,

    L = 4 + 3B

    If the area of the rectangle is 15 cm2

    Area = LB = 15

    B (4 + 3B) = 15

    3B² + 4B - 15 = 0

    3B² - 5B + 9B - 15 = 0

    B (3B - 5) + 3 (3B - 5) = 0

    (3B - 5) (B + 3) = 0

    3B - 5 = or B + 3 = 0

    B = 5/3 or - 3

    since B cannot be negative, B = 5/3 cm

    2. The ratio of length to width in a rectangle is 2 ∶ 3.

    Let the length be L and the width B

    Then,

    L/B = 2/3

    2B = 3L, B = (3/2) L

    when the area is 150 in2.

    Area = LB = 150

    (3/2) L² = 150

    L² = 150*2:3

    L² = 100

    L = √100

    L = ±10

    since the length cannot be negative, L = 10 in
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