Hi !

I've got some trouble to resolve this problem :

What is the most little surface area for a triangle containing a square of 1mē ?

It is admitted that a square' side is confunded with a triangle' side.

Thank you !

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- Nov 11th 2012, 07:27 AMmathsforceA triangle in a square ?
Hi !

I've got some trouble to resolve this problem :

What is the most little surface area for a triangle containing a square of 1mē ?

It is admitted that a square' side is confunded with a triangle' side.

Thank you ! - Nov 11th 2012, 02:19 PMHallsofIvyRe: A triangle in a square ?
Okay, set up a coordinate system so that your square has vertices at (0, 0), (1, 0), (0, 1), and (1, 1). The smallest area triangle that will fit around that is the right triangle having (0, 0) as the vertex of the right angle and hypotenuse passing through (1, 1). If we call the point at which the hypotenuse touches the x-axis (X, 0) and the point at which it touches the y axis (0, Y), then the area of the triangle is and, using "similar triangles", or .

So the problem becomes "minimize subject to the constraint . - Nov 11th 2012, 11:15 PMearbothRe: A triangle in a square ?
Here comes a slightly different approach:

1. Draw a sketch (see attachment)

2. The grey right triangles and the blue right triangles are similar:

......... and ...........

3. Use proportions:

4. The area of the triangle is calculated by:

Replace the terms x and y by the terms of #2:

Simplify!

5. You have found out (I hope):

Solve for h:

You should come out with

6. Replace h by 2s in the equation at #5:

- Nov 12th 2012, 10:08 AMmathsforceRe: A triangle in a square ?
Thank you for your help but I don't know how to use similar triangles...

How can I do without using this ?