Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A triangle has two corners, $(8,0,3)$ and $(0,8,3)$ and a third curve in space that consists of all points $(8,8,a^{2}+3)$, where $a$ is a real number. Calculate the area of the triangle as a function of $a$, $f(a)$ and determine its minimum value.

share|cite|improve this question
    
Well, I have solved it. No need to worry. – user0233 Apr 18 '13 at 19:12
    
Then, you maybe want to answer your own question? – gerw Apr 18 '13 at 19:13

Find the length of each of the 3 sides: $\sqrt{8^2+8^2} = 4\sqrt{2}, \sqrt{8^2+a^2}, \sqrt{8^2+a^2}$ and use Heron's formula:

$$ s = 2\sqrt{2} + \sqrt{8^2+a^2} f(a) = \sqrt{s(s-4\sqrt{2})(s-\sqrt{8^2+a^2})^2} $$

anf you can minimize $f^2(a)$ for convenience.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.