Bunuel wrote:

A triangle has sides with lengths x – 2, 2x – 3 and x + 1. If the perimeter of the triangle is 20, what is the length of the longest side?

(A) 9

(B) 8

(C) 7

(D) 6

(E) 5

Perimeter \(= (x -2) + (2x-3)+ (x+1) = 20\)

\(x - 2 + 2x - 3 + x + 1 = 20\)

\(4x - 4 = 20\)

\(4x = 20+4 = 24\)

\(x = \frac{24}{4} = 6\)

Lets put value of \(x\) in the above sides to check which side is longest side.

\(x – 2 = 6 - 2 = 4\)

\(2x – 3 = (2*6) - 3 = 12-3 = 9\)

\(x + 1 = 6 + 1 = 7\)

Therefore Sides are \(4,7\) and \(9\).

Longest side \(= 9\)

Answer (A)...