Word problems... gotta love 'em

[beth56374]

"An open rectangular gutter is made by turning up the sides of a piece of metal 20in wide. The area of the cross-section of the gutter in 50?in?^2. Find the depth of the gutter."


I have been thinking that I should begin with the formula for the area of a rectangle... but I'm not really sure what foot I should start on

 

[Deleted member 4993]

"An open rectangular gutter is made by turning up the sides of a piece of metal 20in wide. The area of the cross-section of the gutter in 50?in?^2. Find the depth of the gutter."


I have been thinking that I should begin with the formula for the area of a rectangle... but I'm not really sure what foot I should start on

Start with drawing a sketch - and assigning variable names.

Then perimeter of the gutter (3 sides of the rectangle) = 20"

and area = 50 sq.in.

Now solve for the sides.

 

[beth56374]

Done that part already... now I don't know how to solve for the area of the "gutter". Because before the sides are folded up it is 20in. I hope this makes sense... :?

 

[galactus]

Let the length of a side be x. Since we are turning up two sides, then we have that the bottom would be 20-2x.

The area is then x(20-2x)

But this must equal 50.

\(\displaystyle x(20-2x)=50\)

\(\displaystyle -2x^{2}+20x-50=0\)

\(\displaystyle 2x^{2}-20x+50=0\)

To find the value of the side lengths, x, and therefore the area, solve the quadratic.