Did you make a sketcth?
A trough is to be made by bending a long rectangular piece of tin units wide.
The cross section of the trough is an isosceles trapezoid with sides
making angles of 120° with the base.
Find the length of one of the sides that is bent which give a maximum capacity.
: ½x E L-2x F ½x :
A * - - - - - * - - - - - * - - - - - * B
* | | *
* | _ | *
x * | ½√3x | * x
* | | *
D *-----------* C
: L-2x :
We have isosceles trapezoid .
Let the two slanted side have length
Three of its sides, total units,
. . so: .
Since , then: .
is a right triangle with a 30° angle and hypotenuse
Then: . . . . and: .
We have a trapezoid:
. . one base is: .
. . the other base is: .
. . the height is: .
We have: .
The width of the tin sheet is bent into thirds.