Question

Find the range for the measures for the third side of a triangle with the given measures of two sides. 14 and 23

Answer 1

Given:

Two sides of a triangle are 14 and 23.

To find:

The angle for the measures for the third side of a triangle.

Solution:

If a, b, c are three sides of a triangle, then

$a+b>c$

$a+c>b$

$b+c>a$

It is given that two sides of a triangle are 14 and 23.

Let the third side of the given triangle be c. Then, using the above inequalities, we get

$a+b>c$

$14+23>c$

$37>c$                 ...(i)

Similarly,

$a+c>b$

$14+c>23$

$c>23-14$

$c>9$                 ...(ii)

And,

$b+c>a$

$23+c>14$

$c>14-23$

$c>-9$                 ...(iii)

Using (i), (ii) and (iii), we get

$9<c<37$

Therefore, the range for third side of the triangle is $9<c<37$.