Liam is paid $25/hr at full rate, and $18/hr at a reduced rate. the hours of work are paid at a ratio of 3: 1, full rate : reduced rate. for example, if he worked 4 hours, he would be paid 3 hours at full rate and 1 hour at reduced rate. calculate his pay for 6 hours of work.

4h30min full rate and 1h30 min reduced rate

So, for 6h of work Liam is owed $ 9×25/2+3×18/2=225/2+32=144.5

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