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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
= .
From the proportion
2+x = 2*5 = 10 =============> x = 10-2 = 8.
ANSWER. The distance from the vase to the wall is 8 ft.
Solved.
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Ignore the post by @josgarithmetic, since it is t o t a l l y I R R E L E V A N T.
When you obtain something from @josgarithmetic, be very careful, because, AS A RULE,
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.
He only can create some "white noise" and "dirty wrong solutions" in this forum, that never are useful.