Answer: 1 km by 5 km
Explanation:
Perimeter of green = 2(4) + 2(2)
= 8 + 4
= 12
Let the width of the yellow = w
and the length of the yellow = L
Then Perimeter = 2w + 2L Perimeter of yellow = Perimeter of green
12 = 2w + 2L
Solve for one of the variables (I chose to solve for w)
12 - 2L = 2w
6 - L = w
Area = length × width Area is given as 5
Substitute "w" with 6 - L
5 = L(6 - L)
5 = 6L - L²
L² - 6L + 5 = 0
(L - 1) (L - 5) = 0
L = 1 L = 5
Both answers are positive so both are valid.
Now, solve for w = 6 - L
w = 6 - 1 w = 6 - 5
= 5 = 1
The measurements are the same (1 × 5), depending on which sides you choose to be the width and the Length.
Answer: width = 1, Length = 5 or width = 5, Length = 1