Superlesson
Project 5-3
Geometry
Chapter 5, Area
The Pythagorean Theorem is very important to architects because it involves the measurements of the three sides of a right triangle. Below, you will use simple applications of the Pythagorean Theorem to analyze plans for two different doghouses.
Part A, The Pythagorean Theorem
1. Look at some plans to build a traditional Doghouse at this Web site. You will find the dimensions of the doghouse at the end of the page.
a. Suppose you decided that you wanted to alter the plans so that there was no overhang on the roof. How long would each side of the slanted roof be?
b. Suppose you realized that your dog was too tall to fit in the house as it was designed, but you didn't want to change any other dimensions on the house except the vertical height of the roof. You have also already constructed the 32" x 40" sides for the roof. You decide the roof needs to be 26" tall rather than 18" tall. (See the sketch below.) Will you be able to accomplish this with the roof pieces you have already constructed? If so, how much overhang will there be?
Part B, Special Right Triangles
2. Now look at the plans for Harry and Sal's A-Frame doghouse. The frame shown is an equilateral triangle. Suppose you have a medium-sized dog that is about 2 feet tall, and you want the house be 3'6 tall from the floor to the peak of the roof. You also want a roof overhang of 6" on each side.
a. Sketch a front view of the house.
b. How wide should the floor be, and how long (along the diagonal) should each side of the roof be?
c. Now, suppose you have a very short squat dog, and you want to make the frame of the doghouse an isoceles right triangle with the distance from the floor to the top of the roof 3'. Again, you want the overhang on each side of the roof to be 6". (See illustration below.) How wide should the floor be, and how long (along the diagonal) should each side of the roof be?
