To show: The area function of the kite is .
The kite contains four triangles with finite lengths is shown below,
Use the Pythagoras theorem to find the length AE,
Use the Pythagoras theorem to find the length CE,
The formula to calculate the area of triangle is,
The formula to calculate area of kite,
Thus, the area function of the kite is .
To find: The length of the cross pieces of the kite to maximize the area of the kite.
The length of the two cross pieces are and the of each of the cross pieces.
The given kite frame to be made from six pieces of wood is shown below,
From the part (a), the area function is .
To find the lengths of the cross pieces of the kite which maximize the area of the kite, it needs to draw the graph of the function .
The function contains the variable x is length of the horizontal cross piece.
The local maximum value of the function is the maximum finite value where the value of the function at the any number is greater than to the original function.
The condition for local minimum is,
The graph of the function is shown below.
From the graph of the function shown as Figure (2) the greatest peak of the graph at the point .
Then, the maximum area of the kite is .
The length of the side BD in the figure (1) is,
Substitute 4.979 for x in the value of .
The length of the side AC in the figure (1) is .
Now, substitute 4.979 for x in the length of the side AC.
So, the original value of x is .
Thus, the value of one cross piece is and the other crosspiece is .
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