Question

the perimeter of a rectangle is 12m find the dimensions for which the diagonal is as short as possible

Answer 1

That is a minimization problem! That means finding a function that you want to make a minimum, take a derivative, then set equal to zero.

Answer 2

So, you have to make an equation for your constraint that the perimeter is 12 m. The best way is to say that the rectangle has width x and height y.

Answer 3

Then you need an equation for the diagonal. How can you get that? You should draw a picture and that will help a lot. Once you have the formula for the diameter, you should use the constraint equation to eliminate one of the variables. Then take the derivative and set equal to zero and solve.

Answer 4

What say you Joseph3212?

Answer 5

thats true so
perimetre
\[P=2(x+y)=12\]
\[x+y=6\]
\[y=6-x\]

diagonal
\[D^2=x^2+y^2\]
if we minimize \[D^2\] it will bw the same minimizing D
\[D^2(x)=x^2+(6-x)^2=36-12x+2x^2\]
\[D \prime =-12+4x=0\]
\[x=3,y=3\]