Question

9.
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:

let

length be L and breadth be B

given,

L=2B-8

perimeter P=56 m

we know,

perimeter of a rectangle= 2(L+B)

56 =2(2B-8+B)

56 =2(3B-8)

56 =6B-16

72/6=B

12m=B

and,

L=2(12)-8

=16m

Answer 2

Answer :

›»› The length and breadth of a rectangular field is 16 m and 12 m.

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 of a rectangular field and the breadth of a rectangular field.

Solution :

Let us assume that the breadth of a rectangular field is x m.

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

→ Length = 2x - 8 m.

According to the given question,

As we know that

→ Perimeter of rectangle = 2(length + breadth).

→ 56 = 2(2x - 8 + x)

→ 56 = 2(2x + x - 8)

→ 56 = 2(3x - 8)

→ 56/2 = 3x - 8

→ 28 = 3x - 8

→ 28 + 8 = 3x

→ 36 = 3x

→ x = 36/3

→ x = 12

Therefore,

→ Breadth of a rectangular field = x m.

→ Breadth of a rectangular field = 12 m.

→ Length of a rectangle field = 2x - 8 m.

→ Length of a rectangle field = 2 * 12 - 8

→ Length of a rectangle field = 24 - 8

→ Length of a rectangle field = 16 m.

Hence, the length and breadth of a rectangular field is 16 m and 12 m.

Verification :

→ Perimeter = 2(length + breadth)

→ 56 = 2(16 + 12)

→ 56 = 2(28)

→ 56 = 56

Here, LHS = RHS

Hence Verified !