Question

A hypothetical square grows so that the length of its diagonals are increasing at a rate of 8m/min. How fast is the area of the square increasing when the sides are 8m each.

Answer 1

Answer: The area of the square is increasing at a rate of 90.4 m2/min (square meters/minute)

Step-by-step explanation: Please see the attachments below

Answer 2

Answer:

The area of the square is increasing at 90.51m^2/min

Step by step explanation:

Given;

Change in diagonal length ∆d = 8m/min

Length l = 8m

When l = 8m

d^2 = 2l^2 = 2×8^2 = 128

d = √128

Area of a square = l^2 = (d^2)/2

d = diagonal

Change in area = ∆A = dA/dd

∆A = 2 × d/2 × ∆d = d×∆d

∆A = √128 × 8 = 90.51m^2/min