Question

3. Find the length and perimeter of a rectangle whose:
(1) Area = 312 cm, Breadth = 13 cm
(ii) Area = 29.58 cm, Breadth = 3.4 cm
(iii) Area = 108 m², Breadth = 72 dm.​

Answer 1

Answer:

I) Given :

• Area = 312 cm²
• Breadth = 13 cm

Find :

• Length
• Perimeter

Solution :

As we know the formula for area of rectangle.

Area of rectangle → Length × Breadth

Substituting the values in it, we get

Area → Length × 13

$\sf \longrightarrow Area = Length \times 13$

$\sf \longrightarrow 312 = Length \times 13$

$\implies$ Length → 312/13

$\implies$Length → 24 cm

Now,

★ We know :-

• The length of the rectangle → 24 cm
• The Breadth of the rectangle → 13 cm

★ Have to Find :-

• What's the perimeter of rectangle.

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 24 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 13 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

★ Solution :-

As we know the formula of perimeter of rectangle$.$

Applying it here,

Perimeter of rectangle → 2 ( L + B)

☆ L { length } → 24 cm

☆ B { Breadth } → 13 cm

Substituting the values :-

➹ 2 ( 24 + 13 )

➹ 2 × 37

➹ 74 cm

Hence,

The perimeter of rectangle is 74 cm.

74 cm.

_____________________________

2) Given :

• Area = 29.58 cm²
• Breadth = 3.4 cm

Find :

• Length
• Perimeter

Solution :

As we know the formula for area of rectangle.

Area of rectangle → Length × Breadth

Substituting the values in it, we get

Area → Length × 3.4

$\sf \longrightarrow Area = Length \times 3.4$

$\sf \longrightarrow 29.58 = Length \times 3.4$

$\implies$ Length → 29.58/3.4

$\implies$Length → 8.7 cm

Now,

★ We know :-

• The length of the rectangle → 8.7 cm
• The Breadth of the rectangle → 3.4 cm

★ Have to Find :-

• What's the perimeter of rectangle.

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 8.7 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 3.4 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

★ Solution :-

As we know the formula of perimeter of rectangle$.$

Applying it here,

Perimeter of rectangle → 2 ( L + B)

☆ L { length } → 8.7 cm

☆ B { Breadth } → 3.4 cm

Substituting the values :-

➹ 2 ( 8.7 + 3.4 )

➹ 2 × 12.1

➹ 24.2 cm

Hence,

The permieter of rectangle is 24.2 cm.

_____________________________

3) Given :

• Area = 108 m² or 274.32 cm
• Breadth = 72 cm

Find:

• Length
• Perimeter

Solution :

As we know the formula for area of rectangle.

Area of rectangle → Length × Breadth

Substituting the values in it, we get

Area → Length × 72

$\sf \longrightarrow Area = Length \times 72$

$\sf \longrightarrow 274.32 = Length \times 72$

$\implies$ Length → 274.32/72

$\implies$Length → 3.81 cm

Now,

★ We know :-

The length of the rectangle → 3.81 cm

The Breadth of the rectangle → 72 cm

★ Have to Find :-

• What's the perimeter of rectangle.

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 3.81 cm}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 72 cm}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

★ Solution :-

As we know the formula of perimeter of rectangle$.$

Applying it here,

Perimeter of rectangle → 2 ( L + B)

☆ L { length } → 3.81 cm

☆ B { Breadth } → 72 cm

Substituting the values :-

➹ 2 ( 3.81 + 72 )

➹ 2 × 75.81

➹ 151.62 cm

Hence,

The permieter of rectangle is 151. 62 cm

_____________________________