Question

4.
The lengths of the sides of a triangle are
(2x + 1) cm, (3x + 2) cm and (4x - 1) cm.
(a) Find the perimeter of the triangle in
terms of x.
(b) If the perimeter of the triangle is
47 cm, find the value of x.​

Answer 1

Answer:

a) 9x+2

b) 5

Step-by-step explanation:

2x+1+2-1+3x+4x=9x+2

9x+2 is perimeter

BTP

9x+2=47

9x=47-2

9x=45

x=5

Answer 2

$\underline{ \underline{ \Large \pmb{\sf { {Answer:}} }} }$

a) 9x + 2

a) 9x + 2b) 5

$\underline{ \underline{ \Large \pmb{\sf { {Given:}} }} }$

• The lengths of the sides of a triangle are

(2x + 1) cm, (3x + 2) cm and (4x - 1) cm.

• Perimeter = 47 cm

$\underline{ \underline{ \Large \pmb{\sf { {To \: calculate:}} }} }$

• Find the perimeter of the triangle in terms of x.

• If the perimeter of the triangle is 47 cm, find the value of x.

$\underline{ \underline{ \Large \pmb{\sf { {Calculation:}} }} }$

[a] Perimeter in terms of x.

As per the question,

• Sides of the triangle are (2x + 1) cm, (3x + 2) cm and (4x - 1) cm.

We know that,

$\bigstar \: \boxed{\sf { {Perimeter}_{(\triangle)} = {Sum}_{(All \: side)} }}$

$\longrightarrow \sf 2x + 1 + 3x + 2 + 4x - 1$

$\longrightarrow \sf 2x + 3x + 4x + 1 + 2 - 1$

$\longrightarrow \sf 9x + 3 - 1$

$\longrightarrow \sf 9x + 2$

Therefore, the perimeter of the triangle in

terms of x is 9x + 2.

⠀⠀⠀⠀⠀_____________

[b] Value of x.

$\bigstar \: \boxed{\sf { {Perimeter}_{(\triangle)} = {Sum}_{(All \: side)} }}$

According to the question,

$\longrightarrow \sf {47 = 9x + 2}$

$\longrightarrow \sf {47 - 2= 9x}$

$\longrightarrow \sf {45= 9x}$

$\longrightarrow \sf {\cancel{\dfrac{45}{9}}= x}$

$\longrightarrow \sf { 5= x}$

Therefore,

• Value of x is 5.

$\underline{ \underline{ \Large \pmb{\sf { {More \: about \: triangles !}} }} }$

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

$\sf { \dfrac{1}{2} \times Base \times Height }$