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In the figure, every triangle is a 30∘−60∘−90∘ triangle and, for each pair of triangles, the hypotenuse of the triangle to the right is twice as long as the long leg of the triangle to the left. If the short leg of the smallest triangle is sqrt{3}, what is the value of a?

 

 Jul 20, 2020
 #1
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            Short leg   Long leg  |  Hypotenuse

 

1)               √3                    3                  2√ 3

 

2)                3                    3√3                  6

 

3)              3√3                    9                  6√3  

 

4)                9                    9√3                  18

 

All sides of triangle #3 are 3X the sides of triangle #1. The same is for triangles #4 and #2.

 Jul 20, 2020
 #2
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We have that the long leg of a 30-60-90 trianlge is sqrt3*[short leg] so it is sqrt3*sqrt3*sqrt3*sqrt3 since the *2 and the /2 cancel out so we have (sqrt3)^4/sqrt3 so we have sqrt3^3=3sqrt3 and our final answer is \(\boxed{3\sqrt3}\)

 Jul 21, 2020

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