We can resolve this issue by discovering a feature of the location in regards to x. For this, we observe the adhering to:

$ latex AB+BC= 6$

$ latex x+ BC= 6$

$ latex BC= 6-x$

Then, we can utilize the triangular location formula to obtain:

$ latex A= frac {1} {2} times BC times AB$

$ latex A= frac {1} {2} (6-x) x$

$ latex A= 3x-frac {x ^ 2} {2} $

Now, we need to discover the by-product to develop a formula as well as discover the fixed factors:

$ latex A( x)= 3x-frac {x ^ 2} {2} $

$ latex A'( x)= 3-x$

$ latex 3-x= 0$

$ latex x= 3$

We check whether this factor is an optimum factor utilizing the 2nd acquired:

$ latex A ^ {prime prime} (x)= -1$

Since $latex f ^ {prime prime} (x)

$ latex A= 3x-frac {x ^ 2} {2} $

$ latex A= 3( 3 )- frac {(3 )^ 2} {2} $

$ latex A= frac {9} {2} =4.5$

The optimum location of the triangular is 4.5 centimeters ².



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