Question

The measurements of ONLY ONE of the triangles shown above can be correct. Which one is it?

(REMEMBER, the figures are NOT to scale)

A

B

C

D

Answer 1

Answer:

B

Step-by-step explanation:

B can be correct because sum of any two sides is greater then the other side.

And ther is the case of equal side also available in that.

So if called one correct it has to be B

Answer 2

Answer:

C) Reasons given below

Step-by-step explanation:

Theorems used :-    

1) Sum of two sides in a triangle should be greater than  one side.  

2) Base angles in an isosceles triangle are equal.  

3) Sum of all angles in a triangle should be 180° .  

A) Consider a triangle with vertices A,B and C.(Image attached)

  Now if BA = BC then  

∠A = ∠C = 60°

[Since sum of all angles in a triangle is 180°,And one angle is  60°(Given) .So sum of other two sides = 120.And 120/2 = 60°]

∠A = ∠B = ∠C

It cannot be A since if all angles are equal then it cannot be a isosceles triangle.  

Theorem 2 used.

B)

2.5cm + 3.5cm = 6cm

So, It cannot be a triangle.

Theorem 1 used.

D)  

  100° + 55° +35°  = 190° ≠ 180°  

Theorem 3 used .  

C)  

6 + 4.5 > 7.5  

4.5 + 7.5 > 6  

 6 + 7.5 > 4.5  

Therefore Triangle C can be a triangle.  

So the only answer can be C.  

Hope it helps :)