Asatellite camera takes a rectangular-shaped picture. the smallest region that can be photographed is a 4-km by 4-km rectangle. as the camera zooms out, the length l and width w of the . rectangle increase at a rate of 3 km/sec. how long does it take for the area a to be at least 4 times its original size?

a.) 4.94 sec
b.) 3.28 sec
c.) 9.7 sec
d.) 1.33 sec

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

if you was gonna solve for a, a is a   < -12