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

i need help with this one please

Answer 2

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Answer 3

hypotenuse=sqrt(12^2 4^2)/12

Area=2*L*[sqrt(12^2 4^2)/12]*(1/2)*w

Area =[sqrt(12^2 4^2)/12]*L*w

[sqrt(12^2 4^2)/12])

=4
i gave this as my answer

Answer 4

but this one got wrong

Answer 5

pitch is a ratio not a measurement, unless the roof is vertically 4 feet high and horizontally 12 feet long?

Answer 6

2 * sqrt(run^2+rise^2) * t

Answer 7

I used the term "t" in my previous formula. Looking harder, I now see that "t" is actually a lower-case "L" in script.

So

2 * sqrt(run^2+rise^2) * l

Answer 8

\[s=\frac{\sqrt{10}\times w}{6}\]\[slant\ height=s\]
\[s ^{2}=(\frac{w}{6})^{2}+(\frac{w}{2})^{2}=\frac{10w ^{2}}{36}\]
\[Area=2(l \times s)=2(l \times \frac{\sqrt{10}\times w}{6})=?\]

Answer 9

Area = 2(sqrt 10 wl / 6)

Answer 10

\[Area=\frac{\sqrt{10}\times lw}{3}\]

Answer 11

so 1.05

Answer 12

@LilySwan Not really. The question does not give any values for w and l, either directly or indirectly. The pitch is a ratio and does not have actual dimensions.
The question asks for the area in terms of w and l, therefore the answer is a formula for the area relating to a specific value of pitch.