Question

In each of the following cases, give reason to show that the construction of `Delta ABC` is not possible.
(i) `AB=6` cm, `angleA=45^(@)` and `(BC+AC)=5.8` cm.
(ii) `AB=5` cm, `BC=4` cm and `AC=9` cm.
(iii) `AB=5.4` cm, `angleB=60^(@)` and `(BC-AC)=6` cm.
(iv) `BC=4` cm, `angleA=80^(@), angleB=50^(@)` and `angleC=60^(@)`.

Answer 1

(i) Here `(BC+AC)=5.8` cm and `AB=6` cm.
`:. (BC+AC) lt AB`
Thus, the sum of two sides is not greater than the third side.
Hence, the construction of `Delta ABC` is not possible.
(ii) Here, `(AB+BC)=(5+4) cm =9` cm and `AC=9` cm.
`:. (AB)+BC)=AC`.
Thus, the sum of two sides is not greater than the third side.
Hence, the construction of `Delta ABC` is not possible.
(iii) Here, `(BC-AC)=6` cm and `AB=5.4` cm.
`:. (BC-AC) gt AB`.
Thus, the difference of two sides is not less than the third side.
Hence, the construction of `Delta ABC` is not possible.
(iv) Here, `angleA+angleB+angleC=(80^(@)+50^(@)+60^(@))=190^(@)`.
But, we know that the sum of the angles of a triangle is always `180^(@)`.
Hence, the construction of `Delta ABC` is not possible in this case.