Question

The length of a rectangle exceeds the width by 20 cm .Perimeter of rectangle is 180

centimetre,find Length and width of the rectangle.
​

Answer 1

☆ Given :

• The length of rectangle exeeds the width by 20 cm
• Perimeter of the rectangle = 180 cm

☆ To find :

• The length.
• The breadth.

☆ Solution :

Let the width of the rectangle be x

Then the Length will be x + 20

We know that,

Perimeter (rectangle)= 2(length×breadth)

According to Question,

⟼ 180 = 2( x + 20 + x)

⟼ 180 = 2(2x + 20)

⟼ 180 = 2×2x + 2×20

⟼ 180 = 4x + 40

⟼ 180 - 40 = 4x

⟼ 140 = 4x

⟼ 140/4 = x

⟼ x = 35

Therefore,

• The width of rectangle (x) = 35 cm
• The Length of rectangle (x + 20) = 35+20 = 55 cm.

★ Check :

As we know,

Perimeter of rectangle = 2(l+b)

Thus,

Putting the value :

→ 180 = 2(55 + 35)

→ 180 = 2(90)

→ 180 = 2 × 90

→ 180 = 180

∴ L.H.S. = R.H.S.

Hence, checked !!!

Answer 2

Answer:

Dimensions of the rectangle :

• length = 55cm.
• breadth = 35cm.

Step-by-step explanation :

Question says that, length is 20+ than it's width if the rectangle. The perimeter is 180cm. Find it's dimensions.

Step 1 : Let's assume the dimensions :

➪ breadth = $x$cm.

Since, length is 20 more than the length.

➪ length = $(x + 20)$cm.

Step 2 : Find value of $x$ :

We know that,

Perimeter of a rectangle = 2(l + b)

Here,

• l (length) = $x$cm.
• b (breadth) = $(x + 20)$cm
• perimeter = 180cm (given)

We can say that,

$\implies 180 = 2(x + x + 20)$

Solving for $x$ :

$\implies 180 = 2(2x + 20)$

$\implies 180 = 4x + 40$

$\implies 180 - 40 = 4x$

$\implies 140 = 4x$

$\implies \dfrac{140}{4} = x$

$\implies 35 = x$

$\therefore \sf breadth = { \bf{ \green{35cm.}}}$

Hence, the length will be :

→ (35 + 20)

→ 55cm.