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Manhattan Advanced Geometry Problem Set - Problem #6

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Manhattan Advanced Geometry Problem Set - Problem #6  [#permalink]

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New post 23 Jan 2018, 18:11
I got this problem correct using the similar triangles method.

However, I am trying to understand the book's solution and just do not understand it. Why are we able to use the 7 as a "base" for the larger triangle and the same area (18) for the larger triangle in solving for x?

My thought is that we are "squishing" the triangle with area 18 so that we can make the base 7. But if that's true, I think we would be manipulating the hypotenuse of 12 which was originally used to find the area of the small triangle.
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Re: Manhattan Advanced Geometry Problem Set - Problem #6  [#permalink]

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New post 23 Jan 2018, 19:31
frrcattack wrote:
I got this problem correct using the similar triangles method.

However, I am trying to understand the book's solution and just do not understand it. Why are we able to use the 7 as a "base" for the larger triangle and the same area (18) for the larger triangle in solving for x?

My thought is that we are "squishing" the triangle with area 18 so that we can make the base 7. But if that's true, I think we would be manipulating the hypotenuse of 12 which was originally used to find the area of the small triangle.


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Re: Manhattan Advanced Geometry Problem Set - Problem #6 &nbs [#permalink] 23 Jan 2018, 19:31
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