Question

Two sides of a triangle have lengths 18 cm and 40 cm. Describe the possible lengths of the third side.

Answer 1

depends if it is a right triangle or not and if it is u will use the pothygerem theorem or the distance formula

Answer 2

Here, two side lengths of a triangle given, 18 cm and 40 cm.

We know that, the sum of the lengths of any two sides of a triangle is greater that the third side.

So here, let's take the third side be x.

So we can write ,

$18+40 > x$

$58> x$

$x<58$

Also we can write,

$18+x > 40$

We will get x by subtracting 18 to both sides. We will get,

$18+x -18 >40-18$

$x>40-18$

$x>22$

Also we can write,

$40+x > 22$

As we know 40 >22, so it is obvious 40+x will be greater than 22, as x can not be negative.

So we will take the first two parts, we have got,

$x<58$ and $x>22$

By using both of them, we can write,

$22<x<58$

So we have got the required answer. Possible length of the third side is $22<x<58$.