Word problem: Size of a triangular vent(?)

[foahchon]

I'm having a bit of trouble solving (or even just understanding) a word problem. Here goes:

Kwan is constructing a triangular vent in the gable end of a house. If the pitch of the roof is 6-12 (run 12 ft and rise 6 ft), and the vent must have an area of 4.5ft^2, then what size should he make the base and the height of the triangle?

I really have no idea where to go with this. Any input would be appreciated. Thanks.

 

[tkhunny]

Start with an isosceles triangle. Normally, you would make the fent fit in the top of the roof.

The two congruent sides of the triangle go down each side of the roof.

Where the two sides end, construct a line segment between them. This is the base of your triangle.

construct a perpendicular to the base through the apex of the triangle (the point of the roof). This is the altitiude of the triangle. Call it A.

If the Base of the Triangle measures 2B, then half of it measured B. This is the distance from the end of one of the sides to the middle of the base. Notice how this defines two congruent right triangles.

The last piece you need is the construction information. The roof rises half as far as it moves along. This makes 2A = B.

Just start! You do NOT have to see the solution before you begin. Start drawing. Start calculating. Any time these words cross your mind, "I really have no idea where to go with this," something is seriously wrong and it's probably not your fault. Now, draw that picture and see where it leads.