An 8 ft by 10 ft rectangular floating dock is anchored in a pond. The bow, the front tip of a boat or canoe, is tied to a corner of the dock with a 10-ft rope,
as shown in the diagram below.
a. Sketch a diagram showing the region in which the bow of the canoe can travel
b. What is the area of that region?

where is the figure

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

no solution

step-by-step explanation:

there is not enough information in the problem to solve.