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Constructions — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSConstructions1 Mark
Question
Write True or False in the following. Give reasons for your answer:
A triangle ABC can be constructed in which $\angle\text{B}=105^\circ, \angle\text{C}=90^\circ$ and AB + BC + AC = 10cm.
✓

Answer

False.Solution:
Here, $\angle\text{B}=105^\circ, \angle\text{C}=90^\circ$ and AB + BC + CA = 10cm We know that, sum of angles of a triangle is 180° $\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$ Here, $\angle\text{B}+\angle\text{C}=105^\circ+90^\circ$ $=195^\circ>180^\circ$ which is not true. Thus, $\triangle\text{ABC}$ with given conditions cannot be constructed.

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