Question

A triangle of sides 9 cm, 5 cm and 4 cm can be constructed.

• A. True
• B. False

Answer 1

The correct option is B

False

We know that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Here, 9 cm + 5 cm = 14 cm, which is greater than the side of length 4 cm.

9 cm + 4 cm = 13 cm, which is greater than the side of length 5 cm.

But, 4 cm + 5 cm = 9 cm, which is equal to the remaining side which is of length 9 cm.

Hence this triangle construction is not valid.

[If we try constructing such a triangle, then the point of intersection of the circles of radii 5 cm and 4 cm (drawn with the end points of the side of length 9 cm as centres), happens to lie on the side of length 9 cm. This results in a straight line, and not a triangle].