Hello, mcruz65!

An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide.

The area of the cross-section of the gutter is 50 inē.

Find the depth of the gutter. Code:

* *
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D | | D
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W

The depth of the gutter is $\displaystyle D.$

The width of the gutter is $\displaystyle W.$

We have: .$\displaystyle W + 2D \:=\:20 \quad\Rightarrow\quad W \:=\:20-2D $ .[1]

The area is 50 inē: .$\displaystyle DW \:=\:50$ .[2]

Substitute [1] into [2]: .$\displaystyle D(20-2D) \:=\:50$

. . which simplifies to: .$\displaystyle D^2 - 10D + 25 \:=\:0$

Factor: .$\displaystyle (D-5)(d-5) \:=\:0$

Therefore: .$\displaystyle D = 5$

The depth of the gutter is 5 inches.