Answer:
[tex]\frac{8h}{\sqrt{2}} + 16h[/tex]
Step-by-step explanation:
First we need to compute the side length as a function of h
So x be the side length of the right isosceles triangle, in Pythagorean formula we have
[tex]x^2 + x^2 = h^2[/tex]
[tex]2x^2 = h^2[/tex]
[tex]x = \frac{h}{\sqrt{2}}[/tex]
The cost for the legs is
[tex]C_l = 4*2x = \frac{8h}{\sqrt{2}}[/tex]
The cost for the hypotenuse is
[tex]C_h = 16h[/tex]
So the total cost in term of h is
[tex]C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h[/tex]
The total cost C of construction as a function of h is C = 16 / h + 8√2 / h
The pen is in the shape of an isosceles right angle. This means one of the
angle is 90 degrees and 2 sides of the triangle are equal and the base angles
are equal too.
Using pythagora's theorem
Therefore,
x² + x² = h²
2x² = h²
x² = h² / 2
x = √h²/ √2 = h/√2
cost of the legs = 4 / h/√2 + 4 / h /√2 = 8√2 / h
cost of the hypotenuse = 16 / h
Total cost = 16 / h + 8√2 / h
C = 16 / h + 8√2 / h
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