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Re: ABCD is a square, AD = 6, EB = 6 − 2b, the triangle [#permalink]
1
Since ABCD is a square, it is clear that AB=6.
Therefore, if EB= 6-2b then AE= 2b.
AE is the base of the shaded triangle.
If the probability of a randomly selected point lying in the shaded triangle is 1/3. This will equal the (Area of the shaded triangle/ area of the square).
The area of the square ABDE is 6^2= 36.
Determined by 1/3= Area of triangle/ 36. This will give the area of the triangle to be 12.

The area of the triangle = (2b*2b)/2, which is 2b^2=12.
b^2=6 and therefore the value of b= √6 > 2.
Giving us the the answer A

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ABCD is a square, AD = 6, EB = 6 2b, the triangle [#permalink]
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We are given that side of the square is 6, and that the shaded region is composed of an isos. triangle.

Area of the square is therefore 36. If there is a 1/3 chance of randomly going to the shaded region, it implies that the area of the isos. triangle must be 1/3 of the squares area, which is 12.

If the area of the isos triangle is 12, then that implies that the two legs of the triangle are:
\(x^2/2=24\)
\(x=2\sqrt{6}\)

Since the side of the angle must add up to 6, we know that:
\(2\sqrt{6}+6-2b=6\)
\(2\sqrt{6}=2b\)
\(\sqrt{6}=b\)
Since 2 is equal to root 4, that implies that b is greater than 2, so QA is larger than QB.

A.
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ABCD is a square, AD = 6, EB = 6 2b, the triangle [#permalink]
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