Gavin unwraps the label from around a soup can and finds that it has a width of 10 cm and a
length of 12 cm. The label covers the entire
lateral area of the can and does not overlap. If
the height of the can corresponds to the width of
the label, what is the area of the base of the can
in square centimeters?

europa2433

europa2433

step-by-step explanation:

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+

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