Hi All,
The concept of similar triangles is relatively rare on the GMAT (you likely won't see it more than once on Test Day and you probably won't see it at all). That having been said, the concept is about the ratios of the sides (and how side length effects other things - area, perimeter, other sides, etc.).
Here, we have two triangles with the exact same set of 3 angles, so we know that the two triangles are similar. The one ratio that we're given to work with is that the area of the larger triangle is exactly TWICE that of the smaller triangle. We can use this ratio, along with TESTing VALUES, to get to the solution.
Rather than deal with an abstract triangle, I'm going to say that the small triangle is a 3/4/5 right triangle...
Small Triangle
Area = (1/2)(Base)(Height)
Area = (1/2)(3)(4) = 6
Since the larger triangle has TWICE this area, we know that it's area is 6(2) = 12...
Large Triangle
Area = (1/2)(Base)(Height)
12 = (1/2)(Base)(Height)
Since the triangles are similar, each side of the larger triangle is the same proportionate larger than the corresponding side of the smaller triangle. This means that the two sides (the 3 and the 4) have to each be multiplied by the same number and the result has to DOUBLE the area. The only way to get to DOUBLE is if each side is multiplied by \sqrt{2}
12 = (1/2)(3\sqrt{2})(4\sqrt{2})
In this way, when you multiply everything, you get....
12 = (1/2)(12)(2)
Final Answer:
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Rich
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