Find the value of x. Round your answer to the nearest hundredth if necessary.
First.....find the altitude, A, as.... sqrt (12^2 - 8^2) = sqrt [ 144 - 64 ] = sqrt (80) = 4sqrt 5
And we have this relationship
x / A = A / 8
x / ( 4sqrt 5) = (4sqrt 5) / 8 cross-multiply
8x = (4 sqrt 5)^2
8x = 80
x = 80 / 8 = 10
x = 12 / (8/12) - 8
Using similar triangles
8 is to 12 as 12 is to x + 8
8/12 = 12/(x+8) cross multiply
8x + 64 = 144
x = 10