A triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 cm. Is the given statement true or false and give reasons for your answer.

Solution:

It is given that

In triangle ABC

∠B = 105°

∠C = 90°

AB + BC + AC = 10 cm

From the angle sum property of a triangle

∠A + ∠B + ∠C = 180°

Substituting the values

∠B + ∠C = 105° + 90° = 195°

Here

195° > 180° which is not possible

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 ∠ B = 120°, ∠C = 70° and AB + BC + AC = 20 cm.

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

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NCERT Exemplar Class 9 Maths Exercise 11.2 Problem 5

A triangle ABC can be constructed in which ∠ B = 105°, ∠C = 90° and AB + BC + AC = 10 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 = 105°, ∠C = 90° and AB + BC + AC = 10 cm” is false

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