Question 127206
Let the sides of the rectangular gutter be D (for depth) and the length be L.
From the description we have:
1) 2D+L = 20 and...
2) D*L = 50
Rewrite equation 1) as L = 20-2D and substitute into equation 2).
{{{D(20-2D) = 50}}} Simplify.
{{{20D-2D^2 = 50}}} Subtract 50 from both sides.
{{{20D-2D^2-50 = 0}}} Divide by -2 to ease calculations.
{{{D^2-10D+25 = 0}}} Solve by factoring.
{{{(D-5)(D-5) = 0}}}
So, D = 5
The depth is 5 inches and the length is (20-2(5)) = 10 inches.