Question

6. Find the third side of the triangles whose (a) Two sides : 4 cm, 5 cm; Perimeter = 15 cm (b) Two sides : 6 cm, 9 cm; Perimeter = 20 cm (C) Two sides : 5 cm, 2 cm; Perimeter = 12 cm (d) Two sides : 8 cm, 3 cm; Perimeter = 18 cm (e) Two sides : 8 cm, 5 cm; Perimeter = 24 cm (f) Two sides : 9 cm, 13 cm; Perimeter = 37 cm​

Answer 1

Answer:

Third sides are :

(a) 6 cm.

(b) 5 cm.

(c) 5 cm.

(d) 7 cm.

(e) 11 cm.

(f) 15 cm.

Step-by-step explanation:

We know,

Perimeter of triangle = a + b + c

[Where, a, b ,c are sides of triangle]

(a) Two sides: 4 cm, 5 cm ; Perimeter = 15 cm

Let, Third side be x.

Put sides and perimeter in formula :

→ 4 + 5 + x = 15

→ 9 + x = 15

→ x = 15 - 9

→ x = 6

Thus,

Third side of the triangle is 6 cm.

b) Two sides : 6 cm, 9 cm; Perimeter = 20 cm

Let, Third side be x

Put sides and perimeter in formula :

→ 6 + 9 + x = 20

→ x + 15 = 20

→ x = 20 - 15

→ x = 5

Thus,

Third side of the triangle is 5 cm.

(c)Two sides : 5 cm, 2 cm; Perimeter = 12 cm

Let, Third side be x.

Put sides and perimeter in formula :

→ 5 + 2 + x = 12

→ 7 + x = 12

→ x = 12 - 7

→ x = 5

Thus,

Third side of the triangle is 5 cm.

(d) Two sides : 8 cm, 3 cm; Perimeter = 18 cm

Let, Third side be x.

Put all values in formula :

→ 8 + 3 + x = 18

→ 11 + x = 18

→ x = 18 - 11

→ x = 7

Thus,

Third side of the triangle is 7 cm .

(e) Two sides : 8 cm, 5 cm; Perimeter = 24 cm

Let, Third side be x.

Put sides and perimeter in formula :

→ 8 + 5 + x = 24

→ 13 + x = 24

→ x = 24 - 13

→ x = 11

Thus,

Third side of the triangle is 11 cm.

(f) Two sides : 9 cm, 13 cm; Perimeter = 37 cm

Let, Third side be x.

Put sides and perimeter in formula :

→ 9 + 13 + x = 37

→ 22 + x = 37

→ x = 37 - 22

→ x = 15

Thus

Third side of the triangle is 15 cm.

Answer 2

G I V E N :

Find the third side of the triangles whose

(a) Two sides : 4 cm, 5 cm; Perimeter = 15 cm

(b) Two sides : 6 cm, 9 cm; Perimeter = 20 cm

(c) Two sides : 5 cm, 2 cm; Perimeter = 12 cm

(d) Two sides : 8 cm, 3 cm; Perimeter = 18 cm

(e) Two sides : 8 cm, 5 cm; Perimeter = 24 cm

(f) Two sides : 9 cm, 13 cm; Perimeter = 37 cm

S O L U T I O N :

As we know that Perimeter of a triangle is

$\star \: \underline{ \boxed{ \frak{ \green{{ \sf P}erimeter_{(Triangle)} }= \red{{1}^{st} \: side} + \purple{ {2}^{nd} \: side }+ \pink{ {3}^{rd} \: side} }}}$

Here, in all the six cases we need to find the third side

Case (a)

Two sides : 4 cm, 5 cm; Perimeter = 15 cm

Perimeter = 4 cm + 5 cm + 3rd Side

15 cm = 9 cm + 3rd Side

3rd Side = 15 cm - 9 cm

3rd Side = 6 cm

Case (b)

Two sides : 6 cm, 9 cm; Perimeter = 20 cm

Perimeter = 6 cm + 9 cm + 3rd Side

20 cm = 15 cm + 3rd Side

3rd Side = 20 cm - 15 cm

3rd Side = 5 cm

Case (c)

Two sides : 5 cm, 2 cm; Perimeter = 12 cm

Perimeter = 5 cm + 2 cm + 3rd Side

12 cm = 7 cm + 3rd Side

3rd Side = 12 cm - 7 cm

3rd Side = 5 cm

Case (d)

Two sides : 8 cm, 3 cm; Perimeter = 18 cm

Perimeter = 8 cm + 3 cm + 3rd Side

18 cm = 11 cm + 3rd Side

3rd Side = 18 cm - 11 cm

3rd Side = 7 cm

Case (e)

Two sides : 8 cm, 5 cm; Perimeter = 24 cm

Perimeter = 8 cm + 5 cm + 3rd Side

24 cm = 13 cm + 3rd Side

3rd Side = 24 cm - 13 cm

3rd Side = 11 cm

Case (f)

Two sides : 9 cm, 13 cm; Perimeter = 37 cm

Perimeter = 9 cm + 13 cm + 3rd Side

37 cm = 24 cm + 3rd Side

3rd Side = 37 cm - 22 cm

3rd Side = 15 cm