Width & Depth: rain gutter made by folding up edges of metal

[Cdobson]

A rain gutter is to be made by folding up the edges of a strip of metal. If the metal is 12in. wide and the cross sectional area of the gutter is to be 16 7/8in squared, what are the width and depth of the gutter?

 

[Denis]

Re: Width & Depth

Looks like YOUR job is to find a circle of radius r in which a chord (the width of the gutter)
creates an arc = 12 inches, the chord creating a segment of area 16 7/8 sq.in.

Have a look here: http://mathworld.wolfram.com/CircularSegment.html

 

[Deleted member 4993]

Re: Width & Depth

Without a defined cross-sectional shape (whether circular, trapezoidal, rectangular, etc.) - this is a BAAAAAAAD problem....

 

[soroban]

Hello, Cdobson!

The problem should have been more clearly stated.

A rain gutter is to be made by folding up the edges of a strip of metal.
If the metal is 12 in. wide and the rectangular cross-sectional area
of the gutter is to be 16 7/8 square inches,
what are the width and depth of the gutter?

      *               *
      |               |
    x |               | x
      |               |
      *---------------*
            12-2x

\(\displaystyle \text{The area is: }\:x(12-2x),\,\text{ which will be }16\tfrac{7}{8}\text{ in}^2\)

\(\displaystyle \text{Solve the equation: }\;x(12-2x) \:=\:\frac{135}{8}\)


\(\displaystyle \bigg[\text{I found two solutions: }\;7\tfrac{1}{2} \times 2\tfrac{1}{4}\:\text{ and }\:4\tfrac{1}{2} \times 3\tfrac{3}{4}\bigg]\)