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

To do this problem you basically just have to find the ratio of the hypotenuse of the triangle that the side of the roof forms to the base of the triangle. [ Once you have this, you can form an expression for the roof area using w and L.Relation between hypotenuse and base of roof triangles:hypotenuse=sqrt(12^2 4^2)/12Now that you know this, you can form the expression for the area of the roof:Area=2*L*[sqrt(12^2 4^2)/12]*(1/2)*w—> Area =[sqrt(12^2 4^2)/12]*L*wBasically, there are two sections to the roof. Each section has an area that is dependent upon the length of the roof (L) and the width of that section of the roof (the hypotenuse which equals [sqrt(12^2 4^2)/12]). That value for the hypotenuse can be related to the overall width of the house by multiplying it by (1/2)w, since w represents the entire width of the house. Finally, you multiply that product by 2 to get the total area of the roof because there are two sections.It is kinda hard to explain this without drawing a picture, but hopefully this helps! ]

Answer 2

uh how did you get the numbers?