Question

the length of two sides of a triangle are12cm and 15cm. between what two measures should the length of the third side fall?​

Answer 1

Answer:

Let AB,BC and CA are the sides of triangle ABC

Given that,

Let AB = 15cm, BC = 12cm and Third side CA = ?

Then, We know that

CA = AB − BC

CA = 15 − 12

CA = 3cm.

And

CA = AB + BC

CA = 15 + 12

CA = 27cm.

So the third side CA must lie between 3 < CA < 27cm.

Hence, this is the answer.

Answer 2

Given,

The length of the one side of a triangle is $12 cm$.

The length of the second side of a triangle is $15 cm$.

We know that, the sum of the lengths of any two sides should be greater than the length of the third side in a triangle.

So, the length of the third side should be less than sum of the first and second sides.

Third side$<(12+15)$.

Third side $<27$.   ______$(1)$

And also, the length of the third side should not be less than the difference of the lengths of any two sides in a triangle.

So, the length of the third side should be greater than the difference of first and second sides.

Third side$>(15-12)$

Third side$>3$.   _______$(2)$

From equations $(1)$ and $(2)$, $3<$third side$<27$.

Hence, the length of the third side of the triangle falls between $3 cm$ and $27 cm$.