Question 1136112
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It is about proportions . . . 


You have two similar (right-angled) triangles.


The legs of the smaller triangle are 2 ft and 1 ft, where 1 ft is the height of the vase.


The legs of the greater triangle are (2+x) ft and 5 ft.


The unknown x is the distance of the vase from the wall.


The proportion (from the triangles similarity) is


    {{{1/2}}} = {{{5/(2+x)}}}.


From the proportion


    2+x = 2*5 = 10  =============>  x = 10-2 = 8.


<U>ANSWER</U>.  The distance from the vase to the wall is 8 ft.
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Solved.


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Ignore the post by &nbsp;@josgarithmetic, &nbsp;since it is &nbsp;&nbsp;<U>t o t a l l y  &nbsp;&nbsp;&nbsp;&nbsp;I R R E L E V A N T</U>.




When you obtain something from @josgarithmetic, &nbsp;be very careful, &nbsp;because, &nbsp;<U>AS &nbsp;A &nbsp;RULE</U>,


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    1)  he can not read a problem correctly;

    2)  he can not interpret correctly what he reads;

    3)  he can not solve a problem correctly;

    4)  he can not present a solution correctly.
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He only can create some &nbsp;"white noise" &nbsp;and &nbsp;"dirty wrong solutions" &nbsp;in this forum, &nbsp;that never are useful.