Question

the length of a rectangle is decreasing at a rate of 9 cm/sec while the width is increasing at a rate of 9 cm/sec. l=7 cm and w=24 cm. find the rates of change of the area, the perimeter, and the lengths the diagonals of the rectangle. determine whether these are increasing, decreasing, or constant.

Answer 1

the important thing here would be to find equations that would determine the area, perimeter, and diags with inorder to use this given information

Answer 2

Area = length x width

Area' = (length' x width) + (length x width')
.................................

Perimeter = 2 x length + 2 x width

Perimeter' = 2 x length' + 2 x width'

Answer 3

diag^2 = length^2 + width^2

2 x diag x diag' = 2 x length x length' + 2 x width x width'

diag' = length x length' + width x width'; divided by diag