OpenStudy (anonymous):

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.

5 years ago
OpenStudy (anonymous):

I got as far as doing the Pythagorean Theorem to find the hypotenuse of the triangle that half the run and rise make. Half the run would be 6ft and the rise is 4 ft, so a^2 + b^2 = c^2 6^2 + 4^2 = c^2 36 + 16 = c^2 52 = c^2 √52 = c Aprox. 7.2 = c Now I know I have to figure the length now so that L * 7.2 is the Area of one side of the roof and that multiplied by 2 would equal the area of the whole roof, but I am just stuck and can't figure out how to move on. Any help would be much appreciated!

5 years ago
OpenStudy (radar):

You realize that there is not going to be a numeric solution, that your area is going to be in terms of w and l. Since there is no mention of overhang calculate just one half of the roof area using w, l, and the slope.

5 years ago
OpenStudy (radar):

going for just one half (one side of the roof). Run is w/2. Since the slope is 1:3 then the height (rise) is going to be (w/2)*(1/3) or w/6. Now you can use the pythagorean theorem and calculate the slant height (hypotenuse) of the thing.|dw:1351705764528:dw|

5 years ago