Question

1. the perimeter of the triangle is at most 20.6 centimeters. write and solve an inequality to find the maximum measurement of the unknown side length.

define variable: _______
inequality: _______
solution: _______ (make sure it is an inequality and labeled!!)
6.3 cm
8.4 cm

Explanation:

Step1: Define the unknown variable

Let $x$ = length of the unknown side (in cm).

Step2: Set up perimeter inequality

Sum of sides ≤ max perimeter:
$6.3 + 8.4 + x \leq 20.6$

Step3: Simplify left-hand side

Calculate known side sum:
$14.7 + x \leq 20.6$

Step4: Solve for $x$

Subtract 14.7 from both sides:
$x \leq 20.6 - 14.7$
$x \leq 5.9$

Step5: Apply triangle inequality

Unknown side > difference of known sides:
$x > 8.4 - 6.3$
$x > 2.1$

Answer:

Define variable: Let $x$ = length of the unknown side (in centimeters)
Inequality: $2.1 < x \leq 5.9$
The maximum measurement of the unknown side length is $\boldsymbol{5.9}$ centimeters.