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28 January, 10:11

A rectangle has a perimeter of 20 inches and an area of 24 square inches. What are the length and width of the rectangle?

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Answers (2)
  1. 28 January, 10:47
    0
    Length = 6in

    Width = 4in

    Step-by-step explanation:

    The formula for solving the perimeter of a rectangle is:

    P = 2 (L+W)

    The formula for finding the area of a rectangle is:

    A = L x W

    If we substitute our values, we will get:

    P = 2 (6 + 4)

    P = 2 (10)

    P = 20in

    A = 6 x 4

    A = 24in²
  2. 28 January, 13:22
    0
    When l = 6 ⇒ w = 4

    when l = 4 ⇒w = 6

    Step-by-step explanation:

    We have given perimeter and area of rectangle.

    Perimeter = P = 20 inches and Area = A = 24 square inches

    We have to find the length and width of the rectangle.

    Let l is length and w is width of rectangle.

    The formula of Perimeter is:

    P = 2 (l+w)

    The formula of area is:

    A = l * w

    Given values:

    P = 2 (l+w) = 20

    l+w = 10

    w = 10-l eq (1)

    A = l * w = 24 eq (2)

    Putting eq (1) in eq (2), we have

    A = l * (10-l) = 24

    10l-l² = 24

    l²-10l + 24 = 0

    Applying factorization to above equation, we have

    (l-6) (l-4) = 0

    Applying Zero-Product rule, we have

    l-6 = 0 or l-4 = 0

    l = 6 or l = 4

    Putting above values in eq (1), we have

    When l = 6 ⇒ w = 10-6

    w = 4

    when l = 4 ⇒w = 10-4

    w = 6

    Answer is:

    When l = 6 ⇒ w = 4

    when l = 4 ⇒w = 6
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