##### Need math help with this word problem about a carpenter, and show work

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A carpenter wants to construct a simple cabin with a pitched roof.   The inside height of this “A-frame” cabin next to the wall must be 8 feet high.   The owner wants the inside height of the roof in the middle of the room (at the tallest point) to be 12 feet high.  The owner wants the slope of the roof to be 1/3.   How wide then must the cabin be?

Jan 4th, 2016

Let us consider x axis to represent the floor of the cabin and the y-axis to represent the wall of the room.

We have to determine the equation of the line with slope=1/3 and passing through (0,8)

The equation in the slope -intercept form  is y=x/3 +8,as the y-intercept is 8 and the slope m=1/3

Now determine the xpoint where the height is 12 ft

12=x/3+8

Solve for x

x=12 ft.

The distance from the 8ft to the 12 ft room is 12 ft.So the total width will be twice this distance.

The width of the cabin then will be 12*2 =24 ft(answer)

I hope this would help you,but if you have any doubt regarding this,you can surely ask. :)
Jan 4th, 2016

Jan 4th, 2016

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Jan 4th, 2016
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Jan 4th, 2016
May 29th, 2017
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