In article
<2b51fb1f-b8f1-421b-9f01-0659029a6179@[EMAIL PROTECTED]
>,
baz90@[EMAIL PROTECTED]
wrote:
> Hello all,
> I have just done 35 calculus questions of varying difficulty
> and solved them quite easily, but the last problem i can't get my
> thinking around . This is it: A rectangle PQRS is placed inside
> a scalene triangle ABC [ the diagram is supplied but I can't draw it;
> to explain the diagram.. BC is the base of ABC; P is on AB;Q is on AC;
> S and R are on BC]. If the area of the triangle ABC is constant,
> prove that the maximum area of the rectangle is one-half the area of
> the triangle ABC.
> Hope somebody can even get me started. Thank you. bazza
It should be easy to prove the area of the rectangle can be at least as
large as 1/2 that of the triangle, e.g., when the base of the rectangle
lies on the longest side of the triangle and the other 2 vertices of the
rectangle bisect the other two sides of the triangle.
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