Question

The length of rectangle is 14 cm more than its breadth. If the perimeter is 448 cm, find the dimensions of the rectangle.

Answer 1

ANSWER :

Dimensions are 119 cm and 105 cm.

EXPLANATION :

•GIVEN :-

• Length of rectangle is 14 cm more than its breadth.
• Perimeter of the rectangle is 448 cm.

•TO FIND :

• Dimensions of the rectangle.

•SOLUTION :

Let the breadth of the rectangle be x cm .

Length is 14 cm more than breadth.

So,

$\sf{Length=(x+14)\:cm}$

We know,

${\boxed{\sf{\green{Perimeter\:of\: rectangle=2(Length+Breadth)}}}}$

$\sf{Perimeter=2(l+b)}$

$\implies\sf{Perimeter=2(x+14+x)\:cm}$

$\implies\sf{Perimeter=2(2x+14)\:cm}$

$\implies\sf{Perimeter=4(x+7)\:cm}$

Perimeter = 448 cm

According to the question,

$\sf{4(x+7)=448}$

$\implies\sf{x+7=\frac{448}{4}}$

$\implies\sf{x+7=112}$

$\implies\sf{x=112-7}$

$\implies\sf{x=105}$

Breadth = 105 cm

★Length is 14 cm more than breadth ★

$\sf{Length=(105+14)\:cm}$

$\implies\sf{Length=119\:cm}$

Therefore, dimensions are 119 cm and 105 cm.

______________________________

★VERIFICATION :

Length = 119 cm

Breadth = 105 cm

Perimeter = 2(119+105) cm

→ Perimeter= 448 cm.

Hence verified ____!!

______________________________

MORE INFORMATION :

• Perimeter of rectangle=2(l+b)

• Area of square = (side)²

• Perimeter of square = 4 × side.

• Diagonal of square = side √2

______________________________

Answer 2

Step-by-step explanation:

Given -

• Length of rectangle is 14 cm more than its breadth
• Perimeter = 448 cm

To Find -

Dimension of rectangle

Let x be the breadth of the rectangle.

Then,

The length of the rectangle is (x + 14)

Now,

As we know that,

Perimeter = 2(l + b)

= 448 = 2(x + 14 + x)

= 224 = 2x + 14

= 224 - 14 = 2x

= 210 = 2x

= x = 210/2

• = x = 105 cm

Hence,

The breadth of the rectangle is 105 cm

and

The length of the rectangle is (x + 14) cm

= (105 + 14)

= 119 cm

Verification -

Perimeter = 2(l + b)

= 448 = 2(119 + 105)

= 448 = 2(224)

= 448 = 448

LHS = RHS

Hence,

Verified..

Additional information -

• Area of rectangle = l × b
• Perimeter of rectangle =2(l + b)
• Opposite sides of rectangle is equal.
• Each angle of a rectangle is 90°

here,

l = Length

b = breadth