## anonymous one year ago 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.

1. DanJS

|dw:1437894088928:dw|

2. DanJS

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

3. dumbcow

note that because of line "y=x" ---> h = a Area of small triangle = 1/2 Area of big triangle $\frac{1}{2} a^2 = \frac{1}{2}(\frac{1}{2} 4^2)$ $\frac{1}{2} a^2 = 4$ $a = \sqrt{8} = 2 \sqrt{2}$