The length of the first side of a triangle is a whole number less than 3. THe second side is 3 inches longer than the first, and the third side is 3 inches longer than the second. How many triangles have perimeters less than 36 inches?
2007-09-15 13:12:31 · 4 answers · asked by KB 2 in Science & Mathematics ➔ Mathematics
Let x = the smallest side.
(x) + (x+3) + (x+3+3) < 36
3x + 9 < 36
3x < 27
x < 9
Whole numbers start with 0, but 0 can't be the side of a triangle, so there are still 2 whole numbers less than 3.
1 + 4 + 7 does not work because the sum of any 2 sides of a triangle has to be more than the third side, and 1 + 4 < 7.
2 + 5 + 8 does not work because 2 + 5 < 8.
So... there are none that work.
2007-09-15 13:23:31 · answer #1 · answered by ccw 4 · 0⤊ 1⤋
Well, there are two lengths that fit both conditions for a starting length: "whole number" and "less than 3". Since 0 isn't a valid length, we have 1 and 2.
1 + (1+3) + ((1+3)+3) = 1 + 4 + 7 = 12 < 36
2 + (2+3) + ((2+3)+3) = 2 + 5 + 8 = 15 < 36
2007-09-15 20:23:31 · answer #2 · answered by hogan.enterprises 5 · 0⤊ 2⤋
both
side 1 = 1 inch: side two is 4, and side three is 7. 7+4+1=12
side 1 = 2 inches: side two is 5 and side three is 8. 8+5+2=15
2007-09-15 20:17:57 · answer #3 · answered by BioHazard 5 · 0⤊ 2⤋
Let x = the whole number
Then x-3 = 1st side
the 2nd side is x
The 3rd side is x+3
The perimeter is 3x <36
x<12
so 8,11,14
7,10,13
6,9,12
5,8,11
4,7,10
are the only 5 triangles meeting the requirements
2007-09-15 20:22:36 · answer #4 · answered by ironduke8159 7 · 0⤊ 2⤋