If a triangle is made up of sides that are consecutive even integers and has a perimeter of 54, what is the length of the smallest side?

A. 10
B. 20
C. 14
D. 16



Answer :

To find the length of the smallest side of a triangle with sides that are consecutive even integers and a perimeter of 54, let me guide you step-by-step through the solution:

1. Define the sides of the triangle:
Let's denote the consecutive even integers as [tex]\( x \)[/tex], [tex]\( x+2 \)[/tex], and [tex]\( x+4 \)[/tex].

2. Set up the equation for the perimeter:
The perimeter of a triangle is the sum of its three sides. So, we have the following equation for the perimeter:
[tex]\[ x + (x + 2) + (x + 4) = 54 \][/tex]

3. Combine like terms:
Simplify the equation by adding the [tex]\( x \)[/tex] terms together and the constant terms together:
[tex]\[ 3x + 6 = 54 \][/tex]

4. Isolate the variable [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first subtract 6 from both sides of the equation:
[tex]\[ 3x = 48 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
Divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 16 \][/tex]

6. Identify the smallest side:
Since [tex]\( x \)[/tex] represents the smallest side of the triangle, and we've determined [tex]\( x = 16 \)[/tex], the smallest side is 16.

Therefore, the length of the smallest side of the triangle is:
(d) 16