SOLUTION: A landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?

Question 996106: A landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]
A(x) =

Length of base = ? miles
Length of the other two (equal-length) sides = ? miles each
Thank you
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Done part-way through but not including the derivative & maximization work:

Draw a triangle, base x, height h, the two equal sides each d. Cut x exactly in half forming two of .

The drawing allows you to first form two equations.

Starting with perimeter equation solve for d in terms of x.
This part will be .

Substitute this formula for d into the pythagorean relation ship equation and solve for h:

A(x) will be the area function.
, and now you have a formula for h.

Omitting the differentiation steps but starting with the product rule, I am finding ; and you can continue the maximization process...
Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!

A landowner wishes to use 3 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]
A(x) =

Length of base = ? miles
Length of the other two (equal-length) sides = ? miles each
Thank you

Length of base: x
Sum of equal sides: 3 � x
Length of each equal side:
Using the pythagorean formula: , we get the height (H), as: H =
Area, or A(x): , or

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