Question

Choose the correct alternative answer for the following questions.

(i) If two sides of a triangle are 5 cm and 1.5 cm, the lenght of its third side cannot be . . . . . . . .

(A) 3.7 cm (B) 4.1 cm (C) 3.8 cm (D) 3.4 cm

(ii) In $∆$PQR, If $\angle$ R > $\angle$Q then . . . . . . . .

(A) QR > PR

(B) PQ > PR

(C) PQ < PR
(D) QR < PR

(iii) In $∆$TPQ, $\angle$ T = 65^° , $\angle$ P = 95^° which of the following is a true statement ?

(A) PQ < TP

(B) PQ < TQ
(C) TQ < TP < PQ

(D) PQ < TP < TQ

Answer 1

(i)
According to the triangle inequality "the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side".
Therefore, the lenght of the third side cannot be greater than 3.4 cm.
Hence, the correct option is (D).

(ii) In $∆$PQR, If $\angle$ R > $\angle$Q
∴ PQ > PR (The sides opposite to the greater angle is greater than side opposite to the smaller angle)
Hence, the correct option is (B).

(iii) In $∆$TPQ, $\angle$ T = 65^° , $\angle$ P = 95^°
A triangle can have maximum one obtuse angle.
$\angle$T < $\angle$ P
PQ < TQ (The sides opposite to the greater angle is greater than side opposite to the smaller angle)
Hence, the correct option is (B).