All About Triangles and some other stuff MTH 60 Support September 12, 2007

Right Triangles Right triangles contain one right angle. The relationships between the sides can be summarized as a 2 +b 2 =c 2. Pythagorean triples:( 3, 4, 5),( 5, 12, 13)( 7, 24, 25)( 8, 15, 17) a b c

Triangles The area A of any triangle is equal to one- half the product of any base b and corresponding height h. Formula: A =.5bh

Types of triangles equilateral triangle: all three sides are the same length isosceles triangle: two sides are the same length scalene triangle, none of the sides are the same length

Finding the area of equilateral triangles In this triangle, all three sides are equal. By drawing an altitude, the base is cut in half. To find the height of the altitude, use the Pythagorean theorem: a 2 +b 2 =c 2 (½S) 2 +b 2 =S 2 1/4S 2 +b 2 =S 2 b 2 =[3/4]S 2 b=[(√3)/2]S=height Area=½bh Area= ½(S)([(√3)/2]S) Area= (√3)/4(S) ½ S SS S

Finding the area of isosceles triangles In this triangle, two of the three sides are equal. By drawing an altitude, the base is cut in half. What would you do next? ½ A CC

Yesterday’s problem # 3 You have 100 feet of fencing. You need to create two pens, one that is square (or rectangular) and one that is triangular. What are the dimensions that maximize the area of the two figures?

Yesterday’s problem # 4 You are building a pen that is next a river. Therefore, you only have to build 3 sides. You need a pen with an area of 300 ft 2. What is the least amount of fence you can use?