Question

The area of a square is increasing at the constant rate of 16sq.ft./min. When the perimeter of the square is 36ft, how fast is the perimeter of the square increasing?

Answer 1

The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.

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
`*` side = 36

So, side, a' = 9 ft

We know that area of a square is given by the formula:

`A = side^2 = a^2` (If we let side = a units)

Change in area =

`a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft`

So, side got changed from 8.06ft to 9 ft.

So, perimeter when side was 8.06 ft:

`4 * 8.06 = 32.24\ ft`

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 =
`√(97)` ft = 9.85 ft

Next increase in perimeter = 4 (New side - Old side)

= 4 (9.85 - 9)

= 3.4 ft/min