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(i) 2 cm, 3 cm, 5 cm

(ii) 3 cm, 6 cm, 7 cm

(iii) 6 cm, 3 cm, 2 cm

Answer :

We know that for a triangle, the sum of any two sides must be greater than the third side.

(i) Given sides are 2 cm, 3 cm, 5 cm

(2 + 3) = 5

5 = 5

Hence, the triangle is not possible.

(i) Given sides are 3 cm, 6 cm, 7 cm

(3 + 6) = 9 > 7

(6 + 7) = 13 > 3

(7 + 3) = 10 > 6

Hence, the triangle is possible.

(iii) Given sides are 6 cm, 3 cm, 2 cm

(3 + 2) = 5 < 6

Hence, the triangle is not possible.

- Q.2 Take any point O in the interior of a triangle PQR. Is (i) OP + OQ > PQ? (ii) OQ + OR > QR? (iii) OR + OP > RP?
- Q.3 AM is a median of a \(\triangle \) ABC. Is AB + BC + CA > 2 AM? (Consider the sides of triangles \(\triangle \)ABM and \(\triangle \)AMC.)
- Q.4 ABCD is a quadrilateral. Is AB + BC + CD + DA > AC + BD?
- Q.5 ABCD is a quadrilateral. Is AB + BC + CD + DA < 2(AC + BD)?
- Q.6 The length of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

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