Thursday

April 17, 2014

April 17, 2014

Posted by **Kyle** on Wednesday, November 14, 2012 at 12:10am.

- calculus -
**Reiny**, Wednesday, November 14, 2012 at 10:00amlet each side of the equilateral triangle be 2x

let each side of the square be y

then 6x + 4y = 5

y = (5-6x)/4

Area of triangle:

draw in the altiude, so we have a right angled triangle with hypotenuse 2x and base 1x, by Pythagorus the height is √3x (now do you see why I defined the side as 2x and not x ? )

Area of triangle = (1/2)(2x)√3x = √3x^2

area of square = y^2

Area = √3x^2 + y^2

= √3x^2 + ((5-6x)/4 )^2

= √3x^2 + (1/16) (25 - 60x + 36x^2)

= √3x^2 + 25/16 - (15/4)x + (9/4)x^2

d(Area)/dx = 2√3x - 15/4 + (9/2)x

= 0 for a min of Area

x(2√3 + 4.5) = 3.75

x = 3.75/(2√3+4.5) = appr .4709

so each side of the triangle is 2x = .9417 ft

and each side of the square = (5-6x)/4 = .5437 ft

check my arithmetic, I should have written it out on paper first.

**Related Questions**

math - wire is cut into 2 pieces with one piece 14 feet shorter than other.The ...

Calculus - A piece of wire 40 m long is cut into two pieces. One piece is bent ...

Related rates - A piece of wire 10 feet long is cut into two pieces. One piece ...

Calculus - A wire 4 meters long is cut into two pieces. One piece is bent into a...

Calculus - A piece of wire 12 m long is cut into two pieces. One piece is bent ...

pre calculus - A wire 10m long is cut into 2 pieces. one piece will be cut into ...

Calculus - a piece of wire 12 ft. long is cut into two pieces. one piece is made...

differential calculus - a pc of wire 10feet long is cut into 2 pcs. one piece is...

math - A 2 feet piece of wire is cut into two pieces and once piece is bent into...

calculus - A piece of wire 18 m long is cut into two pieces. One piece is bent ...