Answer:
If length of the field is 30 ft, then width is 120 ft.
If the length of the field is 60 ft, then width is 60 ft.
Step-by-step explanation:
Let us assume the length of the rectangular park = L ft
Let us assume the breadth of the rectangular park = B ft
Now, AREA of the given park = L x B
⇒ L x B = 3,600 sq ft ... (1)
Also, the perimeter of three sides = 180 ft
⇒ 2 L + B = 180 ..... (2)
Now, from (1) and (2), we get:
L x B = 3,600
2 L + B = 180 ⇒ B = 180 - 2 L
Substitute this in(1) , we get:
L x B = 3,600 ⇒ L x (180 - 2 L) = 3600
[tex]\implies 180 L - 2L^2 = 3600\\\implies L^2 -90L + 1800 = 0\\\implies (L-30)(L-60)= 0[/tex]
⇒ L = 30 or L = 60
So, if L = 30 ft , then B = 180 - 2L = 180 - 60 = 120 ft
So, if L = 60 ft , then B = 180 - 2L = 180 - 120 = 60 ft
So, if length of the field is 30 ft, then width is 120 ft.
And if the length of the field is 60 ft, then width is 60 ft.
