Answer:
The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.
Step-by-step explanation:
Given that area of square is increasing at a rate of 16 sq ft/min.
Given that final perimeter is 36ft
Perimeter of a square = 4 [tex]\times[/tex] side = 36
So, side, a' = 9 ft
We know that area of a square is given by the formula:
[tex]A = side^2 = a^2[/tex] (If we let side = a units)
Change in area =
[tex]a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft[/tex]
So, side got changed from 8.06ft to 9 ft.
So, perimeter when side was 8.06 ft:
[tex]4 \times 8.06 = 32.24\ ft[/tex]
Hence, increase in the perimeter when perimeter is 36 ft is = 36 - 32.24 = 3.76 ft
For finding Next increase:
area gets changed from 81 sq ft to 81+16 = 97 sq ft
So, new side = [tex]\sqrt{97}[/tex] ft = 9.85 ft
Next increase in perimeter = 4 (New side - Old side)
= 4 (9.85 - 9)
= 3.4 ft/min
