Question

.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 (for every 3 ft you travel horizontally towards the middle of the roof, you go up 1 ft vertically) . How wide then must the cabin be?

Answer 1

The answer is 24'

Explanation:

Data:

a) (0,8) inside of the short wall.

b) (x(1), 12) middle of the inner roof.

c) (2x(1), y(1)) Height of the tallest wall.

• By applying equation for selling we will get:

y=m*x+b

b= 8

m= 1/3

We get:

y=(1/3)*x+8

• We plug in values of (b) as per data:

y=(1/3)*x+8

12=(1/3)*x1+8

12-8=(1/3)*x1

(1/3)*x1=4

x1=12

• Now plug in data of (c) the remaining values:

y=(1/3)*x+8

y1=(1/3)*2x1+8

y1=(1/3)*2*12+8

y1=8+8

y1=16

So,

2x1=24

Wideth of the cabin is 24'