When finding lengths in similar right triangles you use a proportion because the links of the sides of the triangles are proportionate to each other. So for this problem, you would set up the proportion as 2 over 3 = x over 4.5 (2/3 = x/4.5) . It has to be in that order because the length of side x is proportionate to the link of side x because they both represent the length of the bottom side of the triangle whereas the 3 and the 4.5 are proportionate to each other because they both represent the length of the hypotenuse of each triangle.

Once you have the proportion set up, you cross multiply and then solve for x. So, in our proportion 2/3 = x/4.5 you would do 2 times 4.5 and 3 times x which would leave you with 9 = 3x. Then to solve for x, you would divide by 3 (9 divided by 3 equals 3) so x = 3. Therefore, the length of side x is 3.

May 21st, 2015

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