a living room wall is 11 feet long. a shelf that is 2.5 feet is to be centered on the wall. how much space is there from the edge of the shelf to the corner of the wall?

Divide the length of the wall by 2 to find the center:

11/2 = 5.5 feet.

Divide the length of the shelf by 2 to find the center of the shelf:

2.5 / 2 = 1.25

Subtract the center of the shelf from the center of the wall:

5.5 - 1.25 = 4.25 feet.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

care to share were the trapezoid shown is ?