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Constructions — Maths STD 9 — Question

Gujarat 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 $AB + BC + AC = 10\ cm.$
✓

Answer

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^\circ $
$\angle\text{A}+\angle\text{B}+\angle\text{C}=180^\circ$
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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