Question

the perimeter of a triangle is equal to 12 inches. the length of the longest side is equal to the sum of the other two sides minus 2. if you multiply the shortest side by 3 and add one, it will equal 2 times the longest side. find the side lengths

Answer 1

a + b + c = 12
c = (a + b) - 2.....c - a - b = -2
3a + 1 = 2c

add the first 2 equations
a + b + c = 12
-a - b + c = -2
------------------add
2c = 10
c = 5 <== longest side is 5

sub in 5 for c in the 3rd equation
3a + 1 = 2c
3a + 1 = 2(5)
3a + 1 = 10
3a = 10 - 1
3a = 9
a = 3 <== shortest side

now sub in 5 for c and 3 for a back into the first equation
a + b + c = 12
3 + b + 5 = 12
b + 8 = 12
b = 12 - 8
b = 4 <== other side