Question

1. the perimeter of a triangle is 61 mm. the medium side is 11 mm longer than the shortest, and the longest side is 5 mm less than 3 times the shortest. how long is the shortest side?

Explanation:

Step1: Let the shortest side be $x$ mm.

Let the shortest side length be $x$. Then the medium - side length is $x + 11$ mm, and the longest - side length is $3x-5$ mm.

Step2: Set up the perimeter equation.

The perimeter of a triangle is the sum of the lengths of its sides. So, $x+(x + 11)+(3x-5)=61$.

Step3: Simplify the left - hand side of the equation.

Combine like terms: $x+x + 11+3x-5=(x+x + 3x)+(11 - 5)=5x+6$. So, the equation becomes $5x+6 = 61$.

Step4: Solve for $x$.

Subtract 6 from both sides: $5x+6-6=61 - 6$, which gives $5x=55$. Then divide both sides by 5: $\frac{5x}{5}=\frac{55}{5}$, so $x = 11$.

Answer:

11 mm