Question

Find the length of the longest side of the triangle if the perimeter is 23.

Answer 1

12 units

Explanation:

We are told that the perimeter of this triangle is 23 units. Since the perimeter of a triangle is the sum of its three sides, we right this sum using for each side the expression that they show in the picture.

Perimeter =
`(3x-5)+(2x+1)+4x=23\\3x-5+2x+1+4x=23\\9x-4=23\\9x=23+4\\9x=27\\x=(27)/(9) =3`

Therefore, the value of the unknown "x" which appears in the expressions for all of the three sides, is 3 units.

Then, the side: 3x-5 = 3(3)-5 = 9-5 = 4 units

the side 2x+1 = 2(3)+1 = 6+1 = 7 units

and the side 4x = 4(3) = 12 units (therefore this is the longest side).