The perimeter of a triangle is 73 inches. rest of the quesiton is in the description.

Question

If the second side is 5 inches longer than twice the first side, and the third side is 4 inches less than three times the first side, how long is the SHORTEST SIDE of the triangle?

Answer 1

Let's call the first side a

We know the second side is 5 inches longer, or 5 + a, and the third side is 4 less than 3 of the first, or 3a - 4

Since we know that the perimeter is 73 inches, we can add them all up and have:

73 = a + (5 + a) + (3a - 4)

73 = a + 5 + a + 3a - 4

73 = a + a + 3a + 5 - 4

73 = 5a + 1

In order to find the length of the first (we don't know if it's the shortest yet) side, we move all the a's to one side and all the numbers to the other i.e. we get rid oft he + 1

73 - 1 = 5a + 1 - 1

72 = 5a

14.4 = a

So the first side is 14.4 inches, the second is 14.4 + 5 = 19.4 inches, and the third is 3*14.4 - 4 = 43.2 - 4 = 39.2 inches.

Then our shortest side is the first, which is 14.4 inches.

Answer 2

S= 5 + 2F

or 2F=S-5

F = S/2 -5/2

T=-4+3F

T=-4 + 3(S/2-5/2)

= -4 + 3S/2 -15/2

= 3S/2 -23/2

T>S

3rd side > second side

T>S>F

F=S/2-2.5

there's only 2 equations for 3 unknowns, so there is no unique solution, just an infinite number of solutions, but the smallest side, the first side, is half the second side - 2 1/2 inches.