Question

The length of a rectangular field is 8 meters less than twice its breadth. If the perimeter of
the rectangular field is 56 meters, find its length and breadth?​

Answer 1

Step-by-step explanation:

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Answer 2

Answer :

›»› The length and breadth of the rectangle are

Figure :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.4,2){\bf{\large{x cm}}}\put(7.7,1){\large\sf{B}}\put(9.3,0.7){\bf{\large{(2x - 8) cm}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

Given :

• The length of a rectangular field is 8 meters less than twice its breadth. If the perimeter of the rectangular field is 56 meters.

To Find :

• The length and breadth of rectangle.

Solution :

Let us assume that the breadth of rectangle is x m.

As it is given that the length of a rectangular field is 8 meters less than twice its breadth.

→ 2x - 8.

To find the length and breadth of rectangle, we use the formula:-

❰ Perimeter = 2(l + b) ❱

• Perimeter = 56 m.
• Length = 2x - 8 m.
• Breadth = x m.

According to the given question,

On putting the given values in the formula, we get

⟶ 56 = 2(2x - 8 + x)

⟶ 56 = 2(2x + x - 8)

⟶ 56 = 2(3x - 8)

⟶ 56 = 6x - 16

⟶ 56 + 16 = 6x

⟶ 72 = 6x

⟶ x = 72/6

⟶ x = 12

Therefore,

⟼ Breadth of rectangle = x m.

⟼ Breadth of rectangle = 12 m.

⠀

⟼ Length of rectangle = 2x - 8.

⟼ Length of rectangle = 2 * 12 - 8.

⟼ Length of rectangle = 24 - 8.

⟼ Length of rectangle = 16 m.

Hence, the length and breadth of the rectangle are 12 m and 16 m.

⠀

⠀

Verification :

››› Perimeter of rectangle = 2(l + b)

››› 56 = 2(12 + 16)

››› 56 = 2 * 28

››› 56 = 56

Here LHS = RHS

Hence Verified !