Brainlet here

Can you solve this problem Veeky Forums. I wasted hours in this shit I couldn't solve it. Am I a brainlet?
Pic related it's exercise 52

What class is this for?

Determine whether a square or a triangle gives more surface area for every foot of fence

Make the less efficient shape tiny and the more efficient shape huge.

Calculus I

I need to have both. The problem states you need 2 pens

Oh I got what you mean but still doesn't work

It's an optimization problem. Try some stuff in that area and if you still can't get it I'll help you, but you need to show some work first.

Start by making a square and a triangle with sides of 14.2857ft in length and go from there

Aka what in saying is find the formula for the areas of a triangle and square, then find their max (where is the graph increasing then decreasing) and you should be able to go from there.

if i can figure out what you're saying without taking calculus, does that mean i'm a genius?

But that's the problem. I can't relate the sides of the triangle with the sides of the square.

Prove first that triangles are just inefficient rectangles by noting that by duplicating a triangle they can be arranged to form a parallelogram. Then show that rectangle is a inefficient square. Lastly note that one square is better than two. The result follows

Here's what I've done so far. Can't relate the area of the triangle with its perimeter.

>an actual problem
KEK, and this is where /sci fails.

this is what the stupid questions general is for user

Bump

All sides the same length with the triangle sharing a side with the square.

Yeah it's the only possible solution imo. But can we assume that based on the exercise?

Area of sqare = x^2
Area of equilateral triangle = sqrt(3)*y^2/2
Circumference of square = 4x
Circumference of triangle = 3y
3y+4x=100
x,y >= 0
maximize f(x,y) = x^2+sqrt(3)*y^2/2

Method, check x=0, y=0 and the line connecting those.
x=0 => f(x,y) = 25^2 = 625
y=0 => f(x,y) =~ 481

del f = (2x, sqrt(3)y/2)

taking the scalar product of this and the normal of the line fields:
4x+3y*sqrt(3)/2 = 0
remember 4x+3y = 100 so we get
(100-3y)+3y*sqrt(3)/2 = 0 =>
y = 100/3(sqrt(3)-1)

Nw just plug it in, see if x is valid (0 to 25) and wheather this is a local max or min and then you are set.

Do you want me to fuck your solution for this puzzle up?

>for one pen, a single entire wall can be one of the walls of the other pen.

Not very got at math, but i suppose the most efficient way to maximize the area is by having the two pens sharing one side. The circumference of the pens are then 4x+2sqt((0,5x^2)+h^2)=100 feet

The area of the pens are x^2+xh/2

you can then subistute h with an epression with x from the circumference exquation. and then find the maximum of the area function with the derivate.

Don't know if this is correct though

>Area of equilateral triangle = sqrt(3)*y^2/2
No, area=height*base/2
y*sqrt(3/4)*y/2=y^2*sqrt(3)/4

How do you not do calculus... I'm from the uk and we just start it at like 16 and i dont get how you can learn maths without it source:from uk and physics undergrad

Thanks I'll try once I get home.

True, thanks for pointing that out.

OP reporting in. Fuck the area expression is huge as shit specially when derived. Impossible to solve without the calculator. Have I made a stupid mistake? Could someone try to do it?

use degenerate triangle with area zero along one of the square's fences

Bump