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Activity Discussion Math perimeter of the rectangle

  • perimeter of the rectangle

    Posted by Ayushi on February 16, 2024 at 6:12 pm

    The length of a rectangle is 3 more inches than its breadth. The area of the rectangle is 40 in2. What is the perimeter of the rectangle?

    Bharti replied 1 month, 2 weeks ago 2 Members · 1 Reply
  • 1 Reply
  • Bharti

    Member
    February 24, 2024 at 5:30 pm
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    Let’s assume the breadth of the rectangle is x inches.

    According to the given information, the length of the rectangle is 3 more inches than its breadth, so the length would be (x + 3) inches.

    The area of a rectangle is given by the formula: Area = Length × Breadth.

    Plugging in the values we have, we can set up the equation:
    40 = (x + 3) × x

    Expanding the equation:
    40 = x^2 + 3x

    Rearranging the equation into a quadratic form:
    x^2 + 3x – 40 = 0

    Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring gives us:
    (x + 8)(x – 5) = 0

    Setting each factor to zero:
    x + 8 = 0 or x – 5 = 0

    Solving these equations gives us:
    x = -8 or x = 5

    Since the breadth cannot be negative, we discard the solution x = -8.

    Therefore, the breadth of the rectangle is x = 5 inches, and the length is x + 3 = 5 + 3 = 8 inches.

    The perimeter of a rectangle is given by the formula: Perimeter = 2 × (Length + Breadth).

    Plugging in the values we have:
    Perimeter = 2 × (8 + 5) = 2 × 13 = 26 inches.

    So, the perimeter of the rectangle is 26 inches.

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