tag:blogger.com,1999:blog-6986082220402081615.post263827588547905059..comments2023-04-24T08:10:28.755-07:00Comments on Math for Liberal Arts: The triangle inequality and Heron's Formula with LOTS of practice problems.Prof. Hubbardhttp://www.blogger.com/profile/16575880031145705761noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6986082220402081615.post-60670038726171918282011-03-30T05:53:05.385-07:002011-03-30T05:53:05.385-07:00Part 1. For all these examples, determine if the l...Part 1. For all these examples, determine if the lengths can create a triangle (answer YES), a straight line (answer STRAIGHT) or not a triangle (answer NO).<br /><br />a) 1, 1, 1 YES<br />b) 1, 1, 2 STRAIGHT<br />c) 1, 1, 3 NO<br />d) 1, 1, 4 NO<br />e) 1, 2, 2 YES<br />f) 1, 2, 3 STRAIGHT<br />g) 1, 2, 4 NO<br />h) 1, 3, 3 YES<br />i) 1, 3, 4 STRAIGHT<br />j) 1, 4, 4 YES<br />k) 2, 2, 2 YES<br />l) 2, 2, 3 YES<br />m) 2, 2, 4 STRAIGHT<br />n) 2, 3, 3 YES<br />o) 2, 3, 4 YES<br />p) 2, 4, 4 YES<br />q) 3, 3, 3 YES<br />r) 3, 3, 4 YES<br />s) 3, 4, 4 YES<br />t) 4, 4, 4 YES<br /><br />Part 2.<br />For every triplet of numbers that is a triangle, find the area as a square root and rounded to the nearest thousandth.<br /><br />a) 1, 1, 1 YES<br />p = 3, s = 1½<br /><b>Area = sqrt(3)/4 ~= 0.433</b><br /><br />e) 1, 2, 2 YES<br />p = 5, s = 2½<br /><b>Area = sqrt(15)/4 ~= 0.986</b><br /><br />h) 1, 3, 3 YES<br />p = 7, s = 3½<br /><b>Area = sqrt(35)/4 ~= 1.479</b><br /><br />j) 1, 4, 4 YES<br />p = 9, s = 4½<br /><b>Area = 3*sqrt(7)/4 ~= 1.984</b><br /><br />k) 2, 2, 2 YES<br />p = 6, s = 3<br /><b>Area = sqrt(3) ~= 1.732</b><br /><br />l) 2, 2, 3 YES<br />p = 7, s = 3½<br /><b>Area = 3*sqrt(7)/4 ~= 1.984</b><br /><br />n) 2, 3, 3 YES<br />p = 8, s = 4<br /><b>Area = 2*sqrt(2) ~= 2.828</b><br /><br />o) 2, 3, 4 YES<br />p = 9, s = 4½<br /><b>Area = 3*sqrt(15)/4 ~= 2.905</b><br /><br />p) 2, 4, 4 YES<br />p = 10, s = 5<br /><b>Area = sqrt(15) ~= 3.873</b><br /><br />q) 3, 3, 3 YES<br />p = 9, s = 4½<br /><b>Area = 9*sqrt(3)/4 ~= 3.897</b><br /><br />r) 3, 3, 4 YES<br />p = 10, s = 5<br /><b>Area = 2*sqrt(5) ~= 4.472</b><br /><br />s) 3, 4, 4 YES<br />p = 11, s = 5½<br /><b>Area = 3*sqrt(55)/4 ~= 5.562</b><br /><br />t) 4, 4, 4 YES<br />p = 12, s = 6<br /><b>Area = 4*sqrt(3) ~= 6.928</b>Prof. Hubbardhttps://www.blogger.com/profile/16575880031145705761noreply@blogger.com