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December 22, 2014

December 22, 2014

Posted by **david** on Tuesday, December 13, 2011 at 5:31pm.

- geometry -
**Reiny**, Tuesday, December 13, 2011 at 5:57pmlet the base be 2x ,(if x = 1/2 the base)

and let each of the equal sides be y

so we know 2x + 2y = 30

x+y = 15, or y = 15-x

let the height of the triangle be h

then h^2 + x2 = y^2

h^2 + x^2 = (15-x)^2

h^2 + x^2 = 225 - 30x + x^2

h = √(225-30x)

area = (1/2)base x height

= (1/2)(2x)(√(225-30x) )

= x (225-30x)^(1/2)

d(area) = x(1/2)(225-30x)^(-1/2) (-30) + (225-30x)^(1/2)

=0 for a max of area

(225-30x)^(1/2) = 15x/(225-30x)^(1/2)

cross-multiply

15x = 225-30x

45x = 225

x = 5

then h = √(225-150) = √75

and since x+y = 15

y = 10

so each side of the triangle must be 10 yds

and the largest area is (1/2)(10)(√75)

= 25√3

Makes sense that the triangle of largest area would be an equilateral triangle, just like the largest quad would be a square, etc.

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