# CBSE NCERT Solutions for Class 7 Chapter 6

NCERT Solutions are the most important and foremost tool to look up to especially when students are preparing for school and competitive examinations. NCERT Solutions involve detailed solutions of all NCERT textbook questions.

CBSE NCERT Solutions for Class 7 Maths Chapter 6:

Question-1:

Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5cm
(ii) 3 cm, 6 cm, 7cm
(iii) 6 cm, 3 cm, 2cm

Solution:

Since, a triangle is possible whose sum of the lengths of any two sides would be greater than the length of third side.
(i) 2 cm, 3 cm, 5cm (ii) 3 cm, 6 cm, 7cm
2 + 3 > 5 No 3 + 6>7 Yes
2 + 5>3 Yes 6 + 7>3 Yes
3 + 5>2 Yes 3 + 7>6 Yes
This triangle is not possible. This triangle is possible.

(iii) 6 cm, 3 cm, 2 cm
6 + 3 >2 Yes
6 + 2>3 Yes
2 + 3>6 No
This triangle is not possible

Question-2:

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

Solution:

Since, the sum of lengths of any two sides in a triangle should be greater than the length of third side.
It is given that two sides of triangle are 12 cm and 15 cm. Therefore, the third side should be less than 12 + 15 = 27cm.
And also the third side cannot be less than the difference of the two sides. Therefore, the third side has to be more than 15 – 12 = 3cm.
Therefore, the third side could be the length more than 3 cm and less than 27cm

Question-3:

In triangle PQR, D is the mid-point of QR
PM is ------------------
PD is
Is QM = MR?

Solution:

Given: QD = DR
∴ PM is altitude.
PD is median.
No, QM ≠ MR as D is the mid-point of QR.