Hello, dalbir4444!

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. Code:

: ½x E L-2x F ½x :
A * - - - - - * - - - - - * - - - - - * B
* | | *
* | _ | *
x * | ½√3x | * x
*30°| |30°*
* | | *
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: .

Formula: .

We have: .

Maximize

The width of the tin sheet is bent into thirds.