```Question 170729
If we draw the scenario, we might get something like this

<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/house.png" alt="Photobucket - Video and Image Hosting">

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):

{{{drawing(500,500,-0.5,2,-0.5,3.2,

line(0,0,0,3),
line(0,3,2,0),
line(2,0,0,0),
locate(-0.2,1.5,5),
locate(1,-0.2,12),
locate(1,2,x)
)}}}

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^2+b^2=c^2}}} where a and b are the legs of the triangle and c is the hypotenuse

{{{5^2+12^2=x^2}}}  Plug in a=5, b=12, and c=x. Now lets solve for x

{{{2 5 + 1 4 4 =  x  ^ 2}}} Square each individual term

{{{1 6 9 =  x  ^ 2}}} Combine like terms

{{{s q r t ( 1 6 9 ) = s q r t (  x  ^ 2 )}}} 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+1=14}}}

So the board must be 14 m

```