SOLUTION: A builder is about to cut rafters for a roof of a cottage. If the width of the cottage is 24 m and he wants a roof 5 m high with an overhanging eave 1 m, find the total length of t

Algebra ->  Pythagorean-theorem -> SOLUTION: A builder is about to cut rafters for a roof of a cottage. If the width of the cottage is 24 m and he wants a roof 5 m high with an overhanging eave 1 m, find the total length of t      Log On


   

Question 170729: A builder is about to cut rafters for a roof of a cottage. If the width of the cottage is 24 m and he wants a roof 5 m high with an overhanging eave 1 m, find the total length of the rafter.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we draw the scenario, we might get something like this




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So if we look at one side of the roof, we get the triangle (where we let "x" be the length of the roof minus the overhang):






Since we can see that the triangle has legs of 5 and 12 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



5%5E2%2B12%5E2=x%5E2 Plug in a=5, b=12, and c=x. Now lets solve for x


2+5+%2B+1+4+4+=++x++%5E+2 Square each individual term


1+6+9+=++x++%5E+2 Combine like terms


s+q+r+t+%28+1+6+9+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


13=x Take the square root of 169 to get 13


x=13 Rearrange the equation


So this means that the hypotenuse of the triangle is 13 units.


Now because we haven't considered the overhang until now, this means that we need to add in the length of 1 to get

13%2B1=14


So the board must be 14 m