A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm. Is the given statement true or false and give reasons for your answer.

Solution:

It is given that

In triangle ABC

AB = 5 cm

∠A = 45°

We know that

A triangle can be constructed if the sum of two sides is greater than the third side

BC + AC = 5 cm which is equal to AB = 5 cm

Therefore, the statement is false.

✦ Try This: Write True or False in each of the following. Give reasons for your answer: A triangle ABC can be constructed in which AB = 4 cm, ∠A = 35° and BC + AC = 6 cm.

It is given that

In triangle ABC

AB = 4 cm

∠A = 35°

We know that

A triangle can be constructed if the sum of two sides is greater than the third side

BC + AC = 6 cm which is greater than AB = 4 cm

Therefore, the statement is true.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 11

NCERT Exemplar Class 9 Maths Exercise 11.2 Problem 3

A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm. Is the given statement true or false and give reasons for your answer.

Summary:

The statement “A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm” is false

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