Question

Please help me answer this question;

1.A metal gutter open at the tops and ends, is bent up from material 30 cm wide to form a rectangular cross section.
a) If the base of the gutter is x cm wide, find the height of the gutter.
b)Show that the area of the gutter cross section is given by A = 15x - x^2/2.

Thanks.

Answer 1

Make a sketch of the cross-section
I would assume the you are bending the 30 cm wide piece so that the two sides of the gutter are of equal height.
then if the base is x cm, then the height must be (30-x)/2 or 15 - x/2 or 15 - (1/2)x

Area = base x height
= x(15 - x/2) = 15x - x^2/2

Answer 2

thank you very much for your help.