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Question 1107740: find x simplify completely 

   /|\
                               / 90\
                              /  |  \
                             /   |x  \
                            /    |    \
                           /   90|90   \
                          /______|______\
                            16      25

Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
find x simplify completely 


                                /|\
                               / 90\
                              /  |  \
                           a /   |x  \ b
                            /    |    \
                           /   90|90   \
                          /______|______\
                            16      25


I denoted "a" and "b" the legs of the largest right-angled triangle. 

Then you have, by applying the Pythagoras to three different participating right-angled triangles, these three equations


a%5E2 = x%5E2+%2B+16%5E2,           (1)

b%5E2 = x%5E2+%2B+25%5E2,           (2)

a%5E2+%2B+b%5E2 = %2816%2B25%29%5E2.       (3)


By adding equations (1) and (2)  and comparing their sum with equation (3), you get this


2x%5E2++%2B+16%5E2+%2B+25%5E2 = %2816%2B+25%29%5E2  ====>

2x%5E2 = %2816+%2B+25%29%5E2+-+16%5E2+-+25%5E2 = 2*16*25  ====>

x%5E2 = 16*25  ====>  x = sqrt%2816%2A25%29 = 4*5 = 20.


Answer.  x = 20.

Solved.