If the area of a right triangle is 15, what is its perimeter?

1 Answer
Apr 23, 2018

Answer:

The perimeter is given as a function of side #a# via #p = a + 30/a + sqrt{a^2 + 30^2/a^2} # which has a minimum at #a=sqrt{30} # and is unbounded, no maximum.

Explanation:

It could be almost anything. Call the sides #a# and #b# and the hypotenuse #c#. Of course

#c^2 =a^2 + b^2 #

We know

#1 /2 a b = 15#

#b = 30/a #

#c^2 = a^2 + (30/a)^2 = a^2 + 900/a^2#

#c = sqrt{ a^2 + 900/a^2 }#

Call the periimeter #p#:

#p = a+b+c = a + 30/a + sqrt{a^2 + 900/a^2} #

That's a function with a minimum at #a=sqrt{ 30}# (for positive #a#) and is unbounded, no maximum.

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