Question

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 .

Answer 1

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:

$28\div 11.2 = 27+x \div x$

Solving this proportion for x implies $x=18$

Now you can solve for m and p using the pythagorean theorem, because both triangles are right:

$m = \sqrt{18^2+11.2^2} =21.2$

Then, we know that the hypothenuse of the big triangle is m+p, so we have

$m+p=\sqrt{(18+27)^2+28^2} = 53$

which implies

$p = 53-p = 53-21.2=31.8$