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In the closed area limited by the graph $y = 4-x^2$, an isosceles triangle is inscribed. The triangle has its top angle in the origin and its base is parallel to the x-axis. Decide the triangle's maximal area.

My question is the following: Why do you draw the triangle as in the picture below and not in any other way?

Andreas
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    How else could I draw this triangle if "its base is parallel to the x-axis"? – zoli May 01 '17 at 14:55
  • @zoli That is not an intuitive answer, for me at least. – Andreas May 01 '17 at 14:58
  • @zoli Sorry if I'm an idiot at math at current, but I will learn sooner or later. – Andreas May 01 '17 at 15:02
  • Set the top vertex in the origin. "In the closed area" means the base should be above the $x$-axis and below the line $y=4$. "Parallel to $x$-axis" - clear. "Inscribed" means two other vertices on the parabola. Otherwise, no more restrictions. The base on the picture goes through $y=3$ is just a coincidence. You can draw it any other way, it is simply an example of a possible triangle (not the one that maximizes the area). – A.Γ. May 01 '17 at 15:06
  • @Sorry, if my comment was not 100% polite. – zoli May 01 '17 at 15:12
  • @zoli It's okay! – Andreas May 01 '17 at 15:20
  • @A.Γ. PS you should paste your comment into an answer, as you answer my question. – Andreas May 01 '17 at 16:08

1 Answers1

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Set the top vertex in the origin. "In the closed area limited by the graph" sounds a little bit sloppy formulated, because the graph itself does not limit any closed area. I guess they mean "limited by the graph and the $x$-axis". Then the base should be above the $x$-axis and below the line $y=4$. "Parallel to $x$-axis" - as it says. "Inscribed" means two other vertices on the parabola. Otherwise, no more restrictions. The base on the picture goes through $y=3$, but it is just a coincidence. You can draw it any other way, it is simply an example of a possible triangle (not likely the one that maximizes the area). When you vary the base all the possible ways between the $x$-axis and the line $y=4$ you'll get different triangles, and you are to find the one with the largest area.

A.Γ.
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