Question

Try to construct a triangle with $ 5cm,8cm{\text{ and 1cm}} $ . Is it possible or not? Why? Give your justification?

Answer 1

Hint: For constructing a triangle only with the three sides, we should follow these conditions. For this we should check the sum of any two sides, if it is greater than the third side then construction will be possible otherwise not. And in this way, we can answer it.

Complete step-by-step answer:
In this question, we have the length of the triangle given $ 5cm,8cm{\text{ and 1cm}} $ . So for solving it we will first name the sides of the triangle as
 $ \Rightarrow AB = 5cm{\text{ , BC = 8cm , AC = 1cm}} $
Now we will check, for this, we will add any two sides and then compare it with the third triangle.
The concept will be, the sum of two sides is always greater than the third one.
So for this on checking it, we get
 $ \Rightarrow AB + BC > AC $
And on equating it, we get
 $ \Rightarrow 5 + 8 > 1 $
Now we will check the other side,
 $ \Rightarrow BC + AC > AB $
And on equating it, we get
 $ \Rightarrow 8 + 1 > 5 $
Now we will check the last pair of the side, we get
 $ \Rightarrow AC + AB > BC $
And on equating it, we get
 $ \Rightarrow 1 + 5 > 8 $ , and from this, we can see that at this condition it does not follow the relation. So from this, we can say that we cannot construct a triangle having the sides given as $ 5cm,8cm{\text{ and 1cm}} $ .
Hence, we cannot construct a triangle with sides $ 5cm,8cm{\text{ and 1cm}} $ .

Note: Since we had seen the three sides. For two sides we should have at least one angle and also there should be two sides. Or we can have at least two angles and one side. By doing this we can check the construction of a triangle having two sides.