The perimeter of a triangle is 72 cm. The first side of the triangle is 2 cm shorter than the second side. The third side is 5 cm longer than the second side. Find the measure of the shortest side.

Answer 1

Answer: 21cm

Assuming x, y, z are three sides of triangle.

Eq1: x + y + z = 72,

Eq2: y - x = 2,

Eq3: z - y = 5

Goal is to find "x" (since it the shortest one), we are going to eliminate "y" and then simplified as two equations and two unknown variables, therefore:

Subtracting of Eq2 from Eq3: z-x = 7, and then subtracting of Eq2 from Eq1 would result: 2x+z = 70. Now, we have two equations:

z-x = 7, and 2x+z =70,

We just subtract these two equations to eliminate "z" and just keep "x" parameter, which now result as 3x =63, and then x = 21.

Others would be y = 23, and z = 28, which are not needed as main question looking for the shortest side.

Answer 2

We can represent this information with an equation in which all the lengths of the triangle sides add up to 72 and x represents the length of each side, in particular the length of side 2

Side 1: x-2

Side 2: x

Side 3: x + 5

x + (x-2) + (x + 5) = 72

Then we solve for x to find the length of side 2, which will then give us the length of each side.

3x +3 =72

3x = 69

x = 23

Side 1: 23-2 = 21

Side 2: 23

Side 3: 23 + 5 = 28

Side 1 is the shortest side, with a length of 21 cm.