Question
A kite frame is to be made from 6 pieces of wood. The four border pieces have been cut 5 and 12. The long center piece is 13. what should the length of the cross pieces be in order to maximize the area of the kite.
Answers
Reiny
If the two top pieces are 5 units each, the bottom pieces are 12 units each, and if the center piece is 13 inches each, you are looking at two right-angled triangles, since
5^2 + 12^2 = 13^2
Thus the length of the cross pieces is fixed as well as the area. So this is not a problem dealing with "maximum" area
the area of each of the two right-angled triangles is
(1/2)(5)12) = 30
so the area of the whole kite is 60 square units
let each height of the triangles be h
(1/2)(13)h = 30
h = 60/13
so the cross piece is 120/13 units long
5^2 + 12^2 = 13^2
Thus the length of the cross pieces is fixed as well as the area. So this is not a problem dealing with "maximum" area
the area of each of the two right-angled triangles is
(1/2)(5)12) = 30
so the area of the whole kite is 60 square units
let each height of the triangles be h
(1/2)(13)h = 30
h = 60/13
so the cross piece is 120/13 units long