Ask Question
28 October, 21:43

A rectangle has an area of 2020cm².

All sides lengths are a whole number.

What is the greatest possible number of centimetres in the perimeter of the rectangle?

+3
Answers (1)
  1. 29 October, 01:01
    0
    Length = 2020 units

    Width = 1 unit

    Step-by-step explanation:

    We know that area of a rectangle = length x width

    We also know that perimeter = (2 x Length) + (2 x Width)

    the goal is to to find Length and Width such that:

    Condition 1: Length x width = 2020

    Condition 2: (2 x Length) + (2 x Width) = maximum possible

    We are also given that both Length and Width are whole numbers, hence we can start by finding the factors of 2020 into prime factors

    Factor 2020: 2 x 2 x 5 x 101

    By observation, we can see that the following combinations of the factors make up the required area of 2020:

    Case 1: (1) x (2) (2) (5) (101) = 1 x 2020 = 2020

    Perimeter = 2 (1 + 2020) = 4042

    Case 2: (2) x (2) (5) (101) = 2 x 1010 = 2020

    Perimeter = 2 (2 + 1010) = 2024

    Case 3: (2) (2) x (5) (101) = 4 x 505 = 2020

    Perimeter = 2 (4 + 505) = 1018

    Case 4: (2) (2) (5) x (101) = 20 x 101 = 2020

    Perimeter = 2 (20 + 101) = 242

    Case 5: (5) x (2) (2) (101) = 5 x 404 = 2020

    Perimeter = 2 (5 + 404) = 818

    Case 6: (2) (5) x (2) (101) = 10 x 202 = 2020

    Perimeter = 2 (10 + 202) = 424

    From the above, it is clear that case 1 yields the largest perimeter
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “A rectangle has an area of 2020cm². All sides lengths are a whole number. What is the greatest possible number of centimetres in the ...” in 📙 Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers