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
<pre>Length of base: x
Sum of equal sides: 3 – x
Length of each equal side: {{{(3 - x)/2}}}
Using the pythagorean formula: {{{a^2 + b^2 = c^2}}}, we get the height (H), as: H = {{{sqrt(9 - 6x)/2}}}

Area, or A(x): {{{(1/2)bh}}}, or {{{(1/2) * x * (sqrt(9 - 6x)/2)}}}
{{{highlight_green(A(x) = x * (sqrt(9 - 6x)/4))}}}