Question 1107740
.
find x simplify completely

 
<pre>

                                /|\
                               / 90\
                              /  |  \
                           a /   |x  \ b
                            /    |    \
                           /   90|90   \
                          /______|______\
                            16      25     
</pre>


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


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


{{{a^2}}} = {{{x^2 + 16^2}}},           (1)

{{{b^2}}} = {{{x^2 + 25^2}}},           (2)

{{{a^2 + b^2}}} = {{{(16+25)^2}}}.       (3)


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


{{{2x^2  + 16^2 + 25^2}}} = {{{(16+ 25)^2}}}  ====>

{{{2x^2}}} = {{{(16 + 25)^2 - 16^2 - 25^2}}} = 2*16*25  ====>

{{{x^2}}} = 16*25  ====>  x = {{{sqrt(16*25)}}} = 4*5 = 20.


<U>Answer</U>.  x = 20.
</pre>

Solved.