In ∆ ABC,
a. AB + BC > AC
b. AB + BC < AC
c. AB + AC < BC
d. AC + BC < AB

Solution:

Given, ABC is a triangle.

We have to choose the correct option.

We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

Let the two sides be AB and BC

Let the third side be AC

So, AB + BC > AC

Therefore, option a is true.

✦ Try This: In △PQR, if ∠P = 60° and ∠Q = 58°, find ∠R (in degrees).

Given, PQR is a triangle.

We have to find the value of ∠R.

By angle sum property of a triangle,

We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.

∠P + ∠Q + ∠R = 180°

60° + 58° + ∠R = 180°

118° + ∠R = 180°

∠R = 180° - 118°

Therefore, ∠R = 62°

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 10

In ∆ ABC, a. AB + BC > AC, b. AB + BC < AC, c. AB + AC < BC, d. AC + BC < AB

Summary:

In ∆ ABC, AB + BC > AC

☛ Related Questions:

• In ∆PQR, a. PQ – QR > PR, b. PQ + QR < PR, c. PQ – QR< PR, d. PQ + PR< QR
• In Fig. 6.8, PB = PD. The value of x is: a. 85°, b. 90°, c. 25°, d. 35°
• Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is: a. Obtuse angled triangle, . . . .