Take the 2-minute tour ×
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.

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|improve this question
What have you tried? –  gerw Apr 18 '13 at 18:59
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

1 Answer 1

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|improve this answer

Your Answer


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.