Question

Find the number a such that the line x = a divides the region bounded by the curves y = x, y = 0, and x = 4 into two regions with equal area. Give your answer correct to 3 decimal places.

Answer 1

set up a couple of equations with similar triangles and areas, or use an integral 0 to a = a to 4, maybe

Answer 2

note that because of line "y=x" ---> h = a

Area of small triangle = 1/2 Area of big triangle
\[\frac{1}{2} a^2 = \frac{1}{2}(\frac{1}{2} 4^2)\]
\[\frac{1}{2} a^2 = 4\]
\[a = \sqrt{8} = 2 \sqrt{2}\]