What is the perimeter of the triangle?
2 answers:
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Answer:
; line D in the options.
Step-by-step explanation:
The set of equations has no solutions if the two lines are parallel. A quick way to create a parallel line is to solve for y, put it in slope-intercept form. Else, as long as the cofficient of x and y are in the same ratio (in this case 1:1), the two lines are parallel, you just have to be careful not to pick the same line again!
The condition makes sure you are still getting lines (else you would get rid of both x and y); the condition
makes sure you're not picking line A again, just written in a different form.
Now that we have the options:
A and C have a different ratio for the coefficient of x and y (2:1 and 1:2) so are not good.
Choice B is just a more complicated way to write the same line, you can see by dividing both sides by 2 and get back x+y=2.
Line D is correct.
Using the method of Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
From
and 
, we find that 
. Then substituting into 
, we find
and substituting these into
, we get
So we have two possible critical points,
, which give extreme values of 
and 
, respectively.
with partial derivatives (set equal to 0)
From
and substituting these into
So we have two possible critical points,