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A long piece of wood of length 2.8 m is broken into 4 pieces with two pieces of length a and the other two pieces of length b. The four pieces are put together to form a rectangle. Find b if your aim is to have a rectangle with the maximum area.

Respuesta :

Answer:

b = 0.7 m

Explanation:

Total length of the wooden rod is given as

[Tex]2a + 2b = 2.8 m[/tex]

so we will have

[tex]a + b = 1.4[/tex]

now we will have

[tex]Area = ab[/tex]

so we have

[tex]A = a(1.4 - a)[/tex]

now to find the maximum area

[tex]\frac{dA}{da} = 0[/tex]

[tex]\frac{dA}{da} = 1.4 - 2a = 0[/tex]

[tex]a = 0.7 m[/tex]

[tex]b = 0.7 m[/tex]

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