Q51. - Algebra 2

Question

The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.

Write three inequalities to express the relationships among the sides of $\mathbf{\Delta ABC}$.

Step-by-Step Solution

Answer

Three inequalities to express the relationships among the sides of $\Delta ABC$are $\mathbf{a}\mathbf{+}\mathbf{b}>\mathbf{c}\mathbf{,}\mathbf{ }\mathbf{a}\mathbf{+}\mathbf{c}>\mathbf{b}$ and $\mathbf{b}\mathbf{+}\mathbf{c}>\mathbf{a}$.

Step 1 – Description of step.

Let the three sides of a triangle be $a, b$and $c$. According to the triangle inequality theorem, the sum of measure of any two sides of a triangle is greater than the measure of third side.

Consider the sum of sides $a$ and $b$ then, $a+b>c$.

Step 2 – Description of step.

Consider two sides $a$, $c$ and third side $b$, then, $a+c>b$.

Step 3 – Description of step.

Consider two sides $b$, $c$and third side $a$, then, $b+c>a$.

 

Therefore, three inequalities to express the relationships among the sides of $\Delta ABC$are $a+b>c,a+c>b$ and $b+c>a$.