Examine the diagram at right. The smaller triangle (inside of the larger triangle) is similar to larger triangle. How can you solve for x? Now , determine the lengths of m and p . Note that when no units are given on measurements , you may assume that all units are the same .

As the exercise says, the triangles are similar. So, we can set up proportions between correspondent sides.In order to solve for x we can set up the proportion between the horizontal and vertical sides:[tex]28\div 11.2 = 27+x \div x[/tex]Solving this proportion for x implies [tex]x=18[/tex]Now you can solve for m and p using the pythagorean theorem, because both triangles are right:[tex]m = \sqrt{18^2+11.2^2} =21.2[/tex]Then, we know that the hypothenuse of the big triangle is m+p, so we have[tex]m+p=\sqrt{(18+27)^2+28^2} = 53[/tex]which implies[tex]p = 53-p = 53-21.2=31.8[/tex]