Question

Two sides of a triangle have lengths $5$ and $8$, and the length of the third side is an integer. What is the greatest possible value of the perimeter of the triangle?

• A. $22$
• B. $24$
• C. $25$
• D. $26$
• E. $27$

Answer 1

Answer: (C)

$25$

The third side rule says that the length of the third side of the triangle in this case must be less than $5+8=13$
Since the length of the third side is an integer, the length must be $12$.

The biggest possible perimeter is then $5+8+12=25$
As we know, perimeter of a triangle is $=1^{st}$ side $+2^{nd}$ side $+3^{rd}$ side.