Question

8. The length of a rectangle is 20 cm more than its breadth. If the perimeter is 100 cm, find the dimensions of the rectangle
​

Answer 1

Answer:

✳ Length(l) of the rectangle = 35cm.

✳ Breadth (b) of the rectangle = 15 cm.

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SOLUTION

GIVEN

1. The  length of a rectangle is 20 cm more than its breadth.
2. The perimeter is 100 cm.

To Find

The dimensions of the rectangle.

Solution

​Let us Assume that the Breadth(b) of the rectangle is x .$\longrightarrow$(1)

∴From the question , length of a rectangle is 20 cm more than its breadth.

$\implies$

Length(l) of the rectangle = x + 20 $\longrightarrow$ (2)

Perimeter of a rectangle = 2(Length + Breadth) = 2(l+b)

Here,

Perimeter is given as 100 cm.

$\implies$

2(x+x+20) = 100

$\implies$

2 ( 2x + 20 ) = 100

$\implies$

4x + 40 = 100

$\implies$

4x = 100 - 40

$\implies$

4x = 60

$\implies$

$\sf x = \dfrac{60}{4}$

$\implies$

x = 15cm.

From Equation (2) ,

Length(l) of the rectangle = x + 20

Here,

x = 15cm.

$\implies$

Length(l) of the rectangle = 15 + 20 = 35cm.

Step-by-step explanation:

Answer 2

Given :-

• Shape = Rectangle
• The length of a rectangle is 20 cm more than its breadth.
• Perimeter of Rectangle = 100cm

To Find :-

• The dimensions of the rectangle.

Solution :-

It is given that the Length of the Rectangle is 20cm more than its breadth , Therefore :

⟼ Breadth of Rectangle = x

⟼ Length of Rectangle = x + 20

According to the Question :

⟹ Perimeter of Rectangle = 2(L + B)

⟹ 100 = 2 ( x + 20 + x )

⟹ 100 ÷ 2 = ( x + 20 + x )

⟹ 50 = 2x + 20

⟹ 50 - 20 = 2x

⟹ 30 = 2x

⟹ 30 ÷ 2 = x

⟹ 15 = x

Therefore :

⟼ Breadth of Rectangle = x = 15cm

⟼ Length = x + 20 = 15 + 20 = 35cm

________________

Verification :-

⟹ Perimeter of Rectangle = 2(L + B)

⟹ Perimeter of Rectangle = 2 ( 35 + 15 )

⟹ Perimeter of Rectangle = 2 × 50

⟹ 100 = 100

Hence Verified

________________

★ Additional Info :

Formulas Related to Rectangle :

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

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