Jermaine has entered a bowling tournament. To prepare, he bowls five games each day and writes down the score of each game,
along with the mean of five scores. He is looking at the scores from one day last week and finds that one of the numbers has
accidentally been erased.
The four remaining scores are 259, 272, 218, and 237. The mean score of the five games is 254. What is the missing score?

The answer is in the photo. I can only upload it to file hosting. link below.

cutt.ly/5zdtAzt

geometry: triangles

solvers

lessons

answers archive

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