Question

A rectangle has an area of 2020cm².

Answer 1

Answer:

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