lola27 wrote:The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateral triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?
A. 169*sqrt3 /3
B. 84.5
C. 75*sqrt3
D. 169*sqrt3 /4
E. 225*sqrt3 /4
Can anyone explain how to solve this? Thanks
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To determine the distance between 2 points, make the distance the hypotenuse of a right triangle.
Then apply the pythagorean formula or -- better yet -- look for a special triangle:
Since PQ is the hypotenuse of a 5-12-13 triangle, PQ=13.
The height of an equilateral triangle creates a 30-60-90 triangle:
The sides of a 30-60-90 triangle are proportioned s : s√3 : 2s.
In ∆WXY, s√3 = 13.
Thus, s = 13/√3 and 2s = 26/√3.
Area = (1/2)bh = (1/2)(26/√3)(13) = 169/√3 = (169√3) / (√3*√3) = (169√3)/3.
The correct answer is
A.
Note that the solution above does not require knowledge of any special formulas.
While knowing formulas can be be helpful, very few are needed to solve most GMAT problems.
Two important take-aways:
1. DRAW your own figures.
2. LOOK for special triangles.
These two strategies -- all by themselves -- are sufficient to solve many GMAT problems.
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