Question

The length of a rectangular plot is 40 more than the breadth and the perimeter of the plot is 92 m, find the dimensions of the plot.
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Answer 1

GiveN :

The length of a rectangular plot is 40 more than the breadth and the perimeter of the plot is 92 m.

To FinD :

The dimensions of the plot.

SolutioN :

Analysis :

Here the formula of perimeter of rectangle is used. Here we can see that the length and the breadth is dependent ob each other. So we have to form equation. Using the perimeter of the rectangle we can solve the equation and get the dimensions.

Formula Required :

Perimeter of rectangle = 2(l + b)

where,

• l is length
• b is breadth

ExplanatioN :

Let us assume that the breadth is "b" m and length is "b + 40" m.

• Perimeter = 92 m

We know that if we are provided with the perimeter of the rectangle and length and breadth are given in the form of equation then our required formula is,

Perimeter of rectangle = 2(l + b)

where,

• l = b + 40 m
• b = b m
• Perimeter = 92 m

Using the required formula and substituting the required values,

☯ According to the question,

⇒ Perimeter of rectangle = 2(l + b)

⇒ 92 = 2(b + 40 + b)

⇒ 92 = 2(2b + 40)

⇒ 92 = 4b + 80

⇒ 92 - 80 = 4b

⇒ 12 = 4b

⇒ 12/4 = b

⇒ 3 = b

∴ b = 3.

The dimensions are :

1. Length = b + 40 = 3 + 40 = 43 m
2. Breadth = b = 3 m

The dimensions of the plot are 43 m and 3 m.

VerificatioN :

Perimeter of rectangle = 2(l + b)

where,

• l = 43 m
• b = 3 m
• Perimeter = 92 m

Using the required formula and substituting the required values,

☯ According to the question,

⇒ Perimeter of rectangle = 2(l + b)

⇒ 92 = 2(43 + 3)

⇒ 92 = 2(46)

⇒ 92 = 2 × 46

⇒ 92 = 92

∴ LHS = RHS.

• Hence verified.

Answer 2

Answer:

The dimensions of the plot are:

Breadth = 3 m

Length = 43 m

Step-by-step explanation:

Let us assume that Breadth of the rectangular plot be x m

Length = (x + 40) m

Given: Perimeter of the plot = 92 m

Formula: P = 2(l + b) unit

According to question:

2(l + b) = 92

→ l + b = 46

→ x + 40 + x = 46

→ 2x = 46 - 40

→ 2x = 6

→ x = 3

∴ The dimensions of the plot:

Breadth = x = 3 m

Length = x + 40 = 3 + 40 = 43 m

Abbreviations used:

P = Perimeter of rectangle

l = Length of rectangle

b = Breadth of rectangle