A triangle ABC can be constructed in which ∠B = 60°, ∠C = 45° and AB + BC + AC = 12 cm. Is the given statement true or false and give reasons for your answer.

Solution:

It is given that

In triangle ABC

∠B = 60°

∠C = 45°

AB + BC + AC = 12 cm

From the angle sum property of a triangle

∠A + ∠B + ∠C = 180°

Substituting the values

∠B + ∠C = 60° + 45° = 105°

Here

105° < 180° which is possible

Therefore, the statement is true.

✦ Try This: Write True or False in each of the following. Give reasons for your answer: A triangle ABC can be constructed in which ∠ B = 50°, ∠C = 35° and AB + BC + AC = 10 cm.

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

NCERT Exemplar Class 9 Maths Exercise 11.2 Problem 6

A triangle ABC can be constructed in which ∠B = 60°, ∠C = 45° and AB + BC + AC = 12 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 ∠ B = 60°, ∠C = 45° and AB + BC + AC = 12 cm” is true

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