The line y = b-x with 0 < b < 4 intersects the y-axis at P and the line x= 4 at S. If the ratio of the area of triangle QRS to the area of triangle QOP is 9:16, what is the value of b? Express the answer as a decimal to the nearest tenth.
Triangles QRS and QOP are similar
Since the areas are in a ratio of 9/16 the scale factor of QRS to QOP = 3/4
Therefore Q = ( [ 4 / ( 4+ 3)] * 4 , 0 ) = [ (4/7) * 4, 0 ] = (16/7, 0)
So....since Q is on y = b -x
Then
0 = b - (16/7)
b = 16/7
