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alimad
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area of a triange 25 Mar 2008, 10:16
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Can someone explain this one. thanks



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area of a triange 25 Mar 2008, 10:30
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Let us say each side of square is x.
As given that AB = AC, due to symmetry it will mean that A is mid point of top portion of square.

Area of Square = x^2

Say D is top most point of square in left hand side (Between B and A).

Then due to Pythagorus theorem

x^2 (BD^2) + x^2/4 (AD^2) = 10^2 (AB^2)
=> x^2 = 80

Answer C.
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alimad
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area of a triange 25 Mar 2008, 10:54
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how did you get this x^2/4

you are dividing the side into 4 pieces. why not x^2/2 (since A is half the length of one of the side)?
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abhijit_sen
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area of a triange 25 Mar 2008, 11:07
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If entire side is x, then its half is x/2. So square of x/2 is x^2/4.
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area of a triange 25 Mar 2008, 16:51
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is 100 the right answer ?
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area of a triange 27 Mar 2008, 05:12
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Choice E.
If you take the triangle inscribed in the square and Ab=10, then it is an equilateral triangle and therefore the base BC=10cms. Area= 10^2=100.
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area of a triange 27 Mar 2008, 08:10
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First of all there is some problem in this post. Although the post says "Area of Triangle", the attached document tells us to calculate "Area of Square".

I assumed that original question does asks for area of square and not triangle. I have provided a detailed explanation above, please go through the same to get the answer.
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area of a triange 27 Mar 2008, 09:46
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dushver
Choice E.
If you take the triangle inscribed in the square and Ab=10, then it is an equilateral triangle and therefore the base BC=10cms. Area= 10^2=100.
Show more

That is not true. The triangle inscribed is NOT equilateral, even though it may look like it. The answer should be 80 or (D).
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area of a triange 27 Mar 2008, 12:54
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One more way of solving this for those who are not convinced.
Use : Apollonius' theorem
https://en.wikipedia.org/wiki/Apollonius'_theorem

Lets say a median (which happened to be perpendicular) is drawn from A to line BC to the point D.
then
AB^2 + AC^2 = 2(AD^2 + BD^2)
or
AB^2 + AC^2 = 2(AD^2 + CD^2)
(I don't say this, it the formula :-D )
CD = BD = AD/2

10^2 + 10^2 = 2(AD^2 + (AD/2) ^ 2)
200 = 2(5/4 AD^2)
AD^2 = 20*4 = 4*5*4.
AD = 4sqrt5.
AD=BC
Since its square, Area = AD*BC = 16*5= 80.
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area of a triange 28 Mar 2008, 05:11
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H is right middle BC
S of the square = AH x BC = 2 x BH x AH = 4 x BH x BH (2)
BH2 + AH2 = 5x BH x BH = 100 => BH x BH = 20 (1)
(1) and (2) => S of the square = 80



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