Question

A carpenter is building a roof on a barn that is w feet wide and ℓ feet long. The roof will be covered by corrugated tin and the carpenter needs to know the area of the roof to estimate the amount of tin to purchase. The roof will have a pitch of 4:12. Find an expression for the area of the roof in terms of w and ℓ feet long. Note: the pitch of a roof is ratio of the rise to the run as in the picture below.

Answer 1

@amistre64

Answer 2

i used to be a carpenter :)

Answer 3

lol :D

Answer 4

"Find an expression for the area of the roof in terms of w and ℓ "

half the width is our run
the rise is our rise
and length just how far we have to go.

all this has to be, is written using "at least" ws and ls? or ONLy ws and ls?

Answer 5

\[\frac{4}{12}=\frac{rise}{width/2}\]
\[\frac{4}{12}\frac{width}{2}=rise\]
\[\frac{width}{6}=rise\]

Answer 6

now that we have the rise in terms of width, we can use the pythag thrm to determine the length of the slanted part of the roof

Answer 7

\[slant=\sqrt{\left(\frac{width}{2}\right)^2+\left(\frac{width}{6}\right)^2}\]

Answer 8

is this making any sense?

Answer 9

yes

Answer 10

slant * length will give us one side area to cover, doubling it gives us the entire roof area

Answer 11

\[Area_{roof}=(2*length)\sqrt{\left(\frac{width}{2}\right)^2+\left(\frac{width}{6}\right)^2}\]

Answer 12

that equation will work as is, so there really is no need to "simplify" it in my view; but im not the one grading it :)

Answer 13

lol ok thanks alot :)

Answer 14

good luck ;)