m**********e
发帖数: 1045 | 1 I really can't figure it out.
Even I take a look at the solution,
the explain looks very intriguing.
seem the interpreter is also trying to " guess" or test to get the Maxium
inscribled Rectangle
Please contribute your best solution
Attached the test and solution link
test:
here!
http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
Solution:
http://mathcounts.org/sites/default/files/u49/2013_State_Compet |
m**********e
发帖数: 1045 | 2 The #28 is also took extraordinary time and attention, it is way more
difficult for middle school student, I personal think, as one of parents!
【在 m**********e 的大作中提到】
: I really can't figure it out.
: Even I take a look at the solution,
: the explain looks very intriguing.
: seem the interpreter is also trying to " guess" or test to get the Maxium
: inscribled Rectangle
: Please contribute your best solution
: Attached the test and solution link
: test:
: here!
: http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
|
n***p
发帖数: 7668 | 3 不是你高估了自己，就是低估了学生们。
【在 m**********e 的大作中提到】
: The #28 is also took extraordinary time and attention, it is way more
: difficult for middle school student, I personal think, as one of parents!
|
m**********e
发帖数: 1045 | 4 As you know, even #28, with every short time to figure out all the
possiblity (using permutation very organised, I think I am get headache of
#28. not because of it is difficult, it is because of very strivtly
logorithm !
【在 n***p 的大作中提到】
: 不是你高估了自己，就是低估了学生们。
|
m**********e
发帖数: 1045 | 5 I really can't figure it out.
Even I take a look at the solution,
the explain looks very intriguing.
seem the interpreter is also trying to " guess" or test to get the Maxium
inscribled Rectangle
Please contribute your best solution
Attached the test and solution link
test:
here!
http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
Solution:
http://mathcounts.org/sites/default/files/u49/2013_State_Compet |
m**********e
发帖数: 1045 | 6 The #28 is also took extraordinary time and attention, it is way more
difficult for middle school student, I personal think, as one of parents!
【在 m**********e 的大作中提到】
: I really can't figure it out.
: Even I take a look at the solution,
: the explain looks very intriguing.
: seem the interpreter is also trying to " guess" or test to get the Maxium
: inscribled Rectangle
: Please contribute your best solution
: Attached the test and solution link
: test:
: here!
: http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
|
n***p
发帖数: 7668 | 7 不是你高估了自己，就是低估了学生们。
【在 m**********e 的大作中提到】
: The #28 is also took extraordinary time and attention, it is way more
: difficult for middle school student, I personal think, as one of parents!
|
m**********e
发帖数: 1045 | 8 As you know, even #28, with every short time to figure out all the
possiblity (using permutation very organised, I think I am get headache of
#28. not because of it is difficult, it is because of very strivtly
logorithm !
【在 n***p 的大作中提到】
: 不是你高估了自己，就是低估了学生们。
|
s****h
发帖数: 3979 | 9 翻到这个旧帖子。
28题，需要做过不少的排列组合题，算得快而且需要思路清楚。
给5分钟估计不少初中生做这题没问题。
给2分钟就难说了。
会做这题，可以当个合格马工了。
29题，有个疑问，就是为什么rectangle一条边一定在三角形长边上？
solution里没有搞Z*W求导等于0，算出Z等于4，应该是考虑到初中生不懂这个。
估计没几个初中生会。
【在 m**********e 的大作中提到】
: I really can't figure it out.
: Even I take a look at the solution,
: the explain looks very intriguing.
: seem the interpreter is also trying to " guess" or test to get the Maxium
: inscribled Rectangle
: Please contribute your best solution
: Attached the test and solution link
: test:
: here!
: http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
|
g**********l
发帖数: 9 | 10 29题答案应该总是三角形面积的一半
钝角三角形
【在 s****h 的大作中提到】
: 翻到这个旧帖子。
: 28题，需要做过不少的排列组合题，算得快而且需要思路清楚。
: 给5分钟估计不少初中生做这题没问题。
: 给2分钟就难说了。
: 会做这题，可以当个合格马工了。
: 29题，有个疑问，就是为什么rectangle一条边一定在三角形长边上？
: solution里没有搞Z*W求导等于0，算出Z等于4，应该是考虑到初中生不懂这个。
: 估计没几个初中生会。
|
g**********l
发帖数: 9 | 11 name three vertices of the triangle as ABC from the top vertex and consider
a rectangle DEFG with D on AB, E,F on BC and G on CA.
Draw a line DH parallel to AC with H on BC. So the area of DEFG equal to
area of DHCG.
So the original problem is equivalent to minimize the sum of areas of ADG
and BHG, both of which are similar to ABC. If the length ratio AD/AB is x,
then the length ratio BD/AB=1-x. So the sum of areas of these two triangle
is x^2+(1-x)^2 times the area of ABC. So the minimal area achieves at x=1/2.
It is easy to find the area of ABC by Heron's Formula for the area of a
triangle.
I guess this solution is much easier than the official one.
【在 m**********e 的大作中提到】
: I really can't figure it out.
: Even I take a look at the solution,
: the explain looks very intriguing.
: seem the interpreter is also trying to " guess" or test to get the Maxium
: inscribled Rectangle
: Please contribute your best solution
: Attached the test and solution link
: test:
: here!
: http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
|
V****n
发帖数: 651 | 12 29题如果用三角半周长面积公式很简单吧
半周长=（10+17+21）/2=24
面积=（24×（24-10）×（24-17）×（24-21））平方根=84
底边高=（84/21）×2=8
长方形如果长为x, 宽为y,用上面小三角和大三角相似得 8/（8-y）=21/x
长方形面积=xy=(21/8)*(8-y)*y=-21/8(y-4)^2 +42
最大值42当y=4
【在 m**********e 的大作中提到】
: I really can't figure it out.
: Even I take a look at the solution,
: the explain looks very intriguing.
: seem the interpreter is also trying to " guess" or test to get the Maxium
: inscribled Rectangle
: Please contribute your best solution
: Attached the test and solution link
: test:
: here!
: http://mathcounts.org/sites/default/files/u49/2013_State_Sprint
|
