Question

Given the lengths of two sides of a triangle, find the range for the length of the third side. (Range means find between which two numbers the length of the third side must fall.) Write an inequality. a 11.5 and 23.6

Answer 1

Answer:

$12.1 < Y < 35.1$

Step-by-step explanation:

Given

Sides: 11.5 and 23.6

Required

Determine the range of the third side

Let the third side with Y

Two of the following conditions must be satisfied to calculate the range of the third side

$11.5 + Y > 23.6$

$23.6+ Y > 11.5$

$11.5 + 23.6 > Y$

We'll solve one after other

1.    $11.5 + Y > 23.6$

$Y > 23.6 - 11.5$

$Y > 12.1$

2.    $23.6+ Y > 11.5$

$Y > 11.5- 23.6$

$Y > -12.1$

3.    $11.5 + 23.6 > Y$

$35.1 > Y$

$Y < 35.1$

Inequalities with negative can't be used' So, we have

$Y > 12.1$ and $Y < 35.1$

Rewrite inequality

$12.1 < Y$   and   $Y < 35.1$

Combine inequality

$12.1 < Y < 35.1$