Question

The length of a rectangular floor is 20 m , more than its breadth . if the perimeter of the floor is 280 m , what is its length​

Answer 1

GiveN:-

The length of a rectangular floor is 20 m more than its breadth.The perimeter of the floor is 280 m.

To FinD:-

Its length.

SolutioN:-

Analysis :

Here the formula for perimeter of rectangle is used. Here we can see that the length and the breadth are dependent on each other. We have to assume the length and the breadth of the rectangle by depending on the given information and then by equating the equation with the given perimeter we can find the length.

Formula Required :

Perimeter of rectangle = 2(l + b)

where,

• l = Length
• b = Breadth

Explanation :

Let us assume that breadth is "b" m and length is "b + 20" m.

• Perimeter = 280 m.

We know that if we are given the perimeter of the rectangle and asked to find the length then our required formula is,

Perimeter of rectangle = 2(l + b)

where,

• l = length = b + 20 m
• b = breadth = b m
• Perimeter = 280 m

By using the required formula and by substituting the respective values,

⇒ Perimeter of rectangle = 2(l + b)

⇒ 280 = 2(b + 20 + b)

⇒ 280 = 2(2b + 20)

⇒ 280 = 4b + 40

⇒ 280 - 40 = 4b

⇒ 240 = 4b

⇒ 240/4 = b

⇒ 60 = b

∴ Breadth = 60 m.

The dimensions are :

• Breadth = b = 60 m
• Length = b + 20 = 60 + 20 = 80 m

The length of the rectangle is 80 m.

VerificatioN:-

Perimeter of rectangle = 2(l + b)

where,

• l = length = 80 m
• b = breadth = 60 m
• Perimeter = 280 m

By using the required formula and by substituting the respective values,

⇒ Perimeter of rectangle = 2(l + b)

⇒ 280 = 2(80 + 60)

⇒ 280 = 2(140)

⇒ 280 = 2 × 140

⇒ 280 = 280

∴ LHS = RHS.

• Hence verified.

Answer 2

GivEn :-

• Length of rectangular plot is 20m more then its breadth.
• Perimeter of rectangular plot is 280m.

To finD :-

• Length of this rectangular plot.

Solution:-

We have given that length of this plot is 20m more than its breadth and perimeter is 280m.

Let suppose that breadth of this plot is x.

Now,

• Length of plot is x+20m
• Breadth of plot is x
• Perimeter of rectangle is 280m.

We know that the formula of perimeter is as :-

• Perimeter of rectangle = 2( l + b )

[ Where, l = length, b = breadth]

Let substitute values in this formula :

Substituting values in formula :-

Perimeter of rectangle = 2( l+b)

=> 280m = 2( x+20 + x)

=> 280m = 2x + 40 +2x

=> 280m = 4x +40

=> 4x = 280 - 40

=> 4x = 240

=> x = 240/4

=> x = 60m

So, the breadth of rectangle is 60m

We had supposed above that length of rectangle is 20m more that its Breadth.

So,

Length of this rectangle is 60+20 = 80m

Our required answer :-

• Length of rectangle is 80m
• Breadth of rectangle is 60m

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