Question

a galvanized iron sheet 64 cm wide is to be bent to form a gutter by turning up vertical strips along each side.how many centimeters should be turned up at each side in order to give a gutter with the maximum cross-sectional area?

Answer 1

2x + y = 64 where x is vertical height of gutter and y = width
and cross sectional area = xy

are you doing calculus leah?

Answer 2

finding derivatives?

Answer 3

oh - you're not here - i didn't check lol
assuming you have:
y = 64 - 2x
so lets find area A in terms of x:

A = xy = x(64 - 2x)
A = 64x - 2x^2
differentiating:
dA/dx = 64 - 4x
this equals 0 for maxim/minm value of the area A
64 - 4x = 0
so x = 16
this gives maximum area
because second derivative is -4 negative

so for maxim area the sheet should be turned up 16 cms at each end