help me with this math question

Test Preparation
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<p>Image</a> - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting</p>

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<p>The probability that is dealt with in this case is where we have an infinite number of points in our sample space. Thus, because we are given that the probabilty that a point from an infinite number of points within the triangle is 1/5, then the area of the triangle must be 1/5 of the whole square (our sample space). </p>

<p>Thus, we are given that the base of the triangle must be 2a thanks to point P, and the height must be a thanks to point Q. So, the area of the triangle is (1/2)(2a)(a) or a^2. Remember that we said that the area of the triangle must be 1/5 the area of the whole square, or 1/5 of 100 (which is 20).</p>

<p>Thus, we now can compute a:
a^2 = 20
a = sqrt(20) = 2*sqrt(5)</p>

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<p>^ why would (2a)(a) = a^2 and not 2a^2?</p>

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<p>^^ because the whole formula for the area of a triangle is (1/2)bh, where b = 2a and h = a. So (1/2)(2a)(a) = a^2.</p>

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<p>darksaber21 srry but the coordinates of point (p) is (10-2a , 0 ) the x value is 10 - 2a ) not 2a</p>

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<p>@ahmed97
The base of the triangle is the distance between points P and T and the x-coordinate of point P is (10-2a) and that of T is (10), the distance between P and T is the difference in their x-coordinates which is equal to 10-(10-2a) = 2a.</p>

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<p>^^ That is pretty much what I was inferring.</p>

<p>You can also picture it like this. The length of the line between the origin and point P plus the length of the base of the triangle equals the length of the base of the square in question, right? Then, to find the length of the base of the triangle, we take the length of the base of the square minus the length of the line between the origin and point P (which is simply 10-2a). So, 10 - (10-2a) = 2a, exactly what SATQuantum said in my defense.</p>