Question

If the lengths of two sides of a right triangle are $5$ and $12$ units, what is the least possible length, in units, of the third side

1. thienthi
The length of the third side of the tringle must lie in between 7 and 7 i.e length of the third side will always be greater than 7 and smaller than 17 according to the properties of a triangle.
According to the given question.
We have a right angled triangle with the two side lengths 5 unit and 12 unit.
From the properties of a triangle we know that ” the sum of the length of the two sides of a triangle is greater than the length of the third side”. Or ” the difference between the two sides of a triangle is less than the length of the third side”.
Let the third side of the triangle be x units.
So, by the properties of a triangle we can say that
12 – 5 < x
⇒ 7 < x
And 12 + 5 > x
⇒ 17 > x
Therefore, the length of the third side of the tringle must lie in between 7 and 7 i.e length of the third side will always be greater than 7 and smaller than 17.