On Wednesday Mr. Miles walked in right at 9/10 of the trail then he walked one eights of the trail back and you stop to rest what fraction of the course with Mr. Miles from the beginning of the trail when he stopped

31/40

Step-by-step explanation:

Given that:

Fraction of the trail walked intulally = 9/10

Fraction of the trail walked back = 1/8 before stopping to rest

His current distance from the beginning :

Distance walked initially - distance walked back

9/10 - 1/8

The L. C. M of 10 and 8 = 80

Hence,

9/10 - 1/8

= (72 - 10) / 80

= 62 / 80

= 31 / 40

Hence, his rest point or position is 31/40 from the beginning of the trail

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+

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