college pre calculus

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.

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  1. 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

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