A gutter is to be made using a 5m long rectangular piece of metal that has to be bent to form the open topper gutter. the cross section of the gutter is an isosceles trapezoid with sides making angles 120 degrees with the base?
If the top width of the gutter is 60 cm, find the dimensions so that the cross sectional area will be a maximum.
If the top width of the gutter is 60 cm, find the dimensions so that the cross sectional area will be a maximum.
1 Answer
![enter image source here]The cross section of the sheet required would have a base length of
Explanation:
Let the base of the isosceles trapezoid have length
Considering one of the isosceles triangles formed at the base of the large isosceles triangle it is seen that
Since the base angle of the trapezoid is constant, the area of the rectangle contained within the large isosceles triangle must be maximised.
Area of rectangle=
For max/min, differentiating Area, say
Checking the second derivative which will be negative for a max turning point,
From ........
By Pythagoras, the side length