Question 191525
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Since the triangles are similar, corresponding sides are in proportion.  That means that the ratio of the shortest side of one of the triangles, namely <i>a</i> to the shortest side of the other triangle, <i>d</i> is the same as the ratio of <i>b</i> to <i>e</i> and <i>c</i> to <i>f</i>.  Since we are given the measures of both of the short sides, we know that this ratio is *[tex \LARGE 3:4] or better for our purposes: *[tex \LARGE  {3 \over 4}]


Since all three ratios are equal, we can establish the proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ {3 \over 4} = {7 \over f}]


Cross-multiply, that is the numerator on the left times the denominator on the right is equal to the denominator on the left times the numerator on the right.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3f = 28]


Solve for <i>f</i>.  


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f = {28 \over 3}]


28 divided by 3 is 9 with a remainder of 1, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f = {28 \over 3} = 9{1 \over 3}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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