Question

1. the side lengths of a triangle are 11.3 centimeters, 14.7 centimeters, and x centimeters. the perimeter of the triangle is less than 44 centimeters. write and solve an inequality to find the possible values of x.

Explanation:

Step1: Write the perimeter formula

The perimeter $P$ of a triangle with side - lengths $11.3$, $14.7$, and $x$ is $P=11.3 + 14.7+x$.
Since $P<44$, we have the inequality $11.3 + 14.7+x<44$.

Step2: Simplify the left - hand side

First, add $11.3$ and $14.7$: $11.3+14.7 = 26$. So the inequality becomes $26+x<44$.

Step3: Solve for $x$

Subtract $26$ from both sides of the inequality: $x<44 - 26$.
$x<18$.
Also, for a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
$11.3 + x>14.7$ gives $x>14.7 - 11.3$, so $x > 3.4$.
And $14.7+11.3>x$, which is always true for positive values of $x$ since $14.7 + 11.3=26$.

Answer:

$3.4