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.
What is the value of b?
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\((4-x)^2:x^2=9:16\\ (4-x):x=3:4\\16-4x=3x\\ 7x=16\\ \color{blue}x=\dfrac{16}{7}\)
\(m=-\frac{4}{4-x}=-\frac{4}{\frac{28-16}{7}}=-2.\overline 3\)
\( b=-m\cdot x=-\frac{16}{7}\cdot -2.\overline 3\)
\(b=5.\overline 3\)
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