Let's look at problem 15 first. It may seem a little crazy with these Xs all over the place but if we look at the right side of the triangle we can see the upper section has a length of 6 and the lower section has a length of 3x. So the right side = 6 + 2x and we can see that the left side also = 6+2x. Thus see both the left and right are the same length but we still do not know the value of X. Since they are the same length we can see that the section on the right side with length of 2x must be the same as the section on the right with length 6. Thus 6=2x or X = 3.
Now problem 16. The small triangle inside the larger one has a sides of 3x, 2x and 5. The larger triangle has sides 6x, 4x and 5x. If you compare the small to the larger triangle each side is doubling. 3x goes to 6x, 2x goes to 4x. Thus the 5 must also double to 10. which means 5*2 = 5x. solving we get x= 2.
hope that helps
Jan 13th, 2015
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