Last edited by SubAtomic; 10-07-2012 at 17:14.
Yeah good spot.
(Original post by Groat)
Think about triangles in a semi-circle with diameter 5. The biggest area is when the triangle is isosceles (or when
is equal to 45 degrees).
Though i would have done it in the following way if differentiation wasn't allowed,
Last edited by raheem94; 10-07-2012 at 17:31.
This is a bit of a strech for secondary school rather than A Level, but it doesn't use differentiation at least. As above, the area is 0.5*x*sqrt(25-x^2) where x is the length of one of the sides (or both
). Square it and ignore the 0.25 to get (25-x^2)*x^2. I think GCSE can find maximum values of quadratics by writing them as (z+a)^2+b, and this quartic is essentially a quadratic in x^2. However, this is still a stretch for GCSE.
(Original post by Tycho)
Q: Find the maximum possible area of a right-angled triangle which has hypotenuse of length 5m.
Is this an optimisation question? I can get close to the answer by trial-and-error, but how do you solve this mathematically?
Edit: the semi-circle thing seems much more reasonable.
Last edited by Hopple; 10-07-2012 at 17:33.
If it is A-level, not even sure if optimisation gets taught in the higher GCSE syllabus. My solution is basically a GCSE answer as far as I am aware. Square numbers and all. If you can optimise the area with pre sixth form knowledge then fair enough.
(Original post by raheem94)
Your solution gives area as 6, while my answer is 6.25.
You certainly can't get the max area in this way, read the other posts.
Suppose it is like groat said, you'd have to notice that the isoc triangle gives the max area and go from there. Which if in context will be second nature depending on what's been going on in class.
Last edited by SubAtomic; 10-07-2012 at 17:55.