Question

Are the following triangles possible? [4 MARKS]
(i) AB = 4 cm, BC = 5.6 cm, AC = 10 cm
(ii) $\angle A$ = 60${}^o$, $\angle B$ = 120${}^o$, $\angle C$ = 30${}^o$
(iii) AB = 5 cm, BC = 7 cm, AC = 11 cm
(iv) $\angle A$ = 60${}^o$, $\angle B$ = 90${}^o$, $\angle C$ = 30${}^o$

Answer 1

Answer with Reason: 1 Mark each

(i) Triangle ABC is not possible. This is because, for any triangle, the sum of two sides should be greater than the third but AB + BC < AC.

(ii) Triangle ABC is not possible. Sum of all angles in a triangle should be 180${}^o$ but here,
$\angle A$$\left({60}^o\right)$ + $\angle B$$\left({120}^o\right)$ + $\angle C$$\left({30}^o\right)$ = 210${}^o$

(iii) Triangle ABC is possible because it satisfies the condition for the formation of a triangle i.e. the sum of two sides should be greater than the third.

(iv) Triangle ABC is possible. Sum of all angles in a triangle should be 180${}^o$ and here,
$\angle A$$\left({60}^o\right)$ + $\angle B$$\left({90}^o\right)$ + $\angle C$$\left({30}^o\right)$ = 180${}^o$