Which estimate is the most reasonable for this problem?

the distance to louisa’s grandparents’ house is 791 miles. louisa and her family have driven 114 miles. how much farther does louisa’s family need to drive?

a.
500 mi

b.
550 mi

c.
600 mi

d.
700 mi

geometry: triangles

solvers

lessons

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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