Question

A wire of length 20m is to be folded in the form of a rectangle. How many rectangles can be formed by folding the wire if the sides are positive integers in metres​

Answer 1

Answer:

The rectangles formed by folding were 5.

Step-by-step explanation:

Given : A wire of length 20 m is to be folded in the form of a rectangle.

To find : How many rectangles can be formed by folding the wire if the sides are positive integers in meters?

Solution :

A wire of length 20 m is to be folded in the form of a rectangle.

i.e, The perimeter of the rectangle is 20 m.

So, P=2$(\text{Length}+\text{Breadth}$

20=2$(\text{Length}+\text{Breadth}$

$\text{Length}+\text{Breadth}$

$\text{Length}=10-\text{Breadth}$

So, The possible integers are

B=1, L=9

B=2, L=8

B=3, L=7

B=4, L=6

B=5, L=5

We cannot take many more as (4,6) and (6,4) were same thing.

So, The rectangles formed by folding were 5.

Answer 2

Answer:

It is given that a wire of length 20 m is to be folded in the form of a rectangle;

∴ we have: Perimeter of the rectangle =20 m

⇒2(Length + Breadth) =20 m

⇒(Length + Breadth) =

2

20

=10 m

Since, length and breadth are positive integers in metres, therefore, the possible dimensions are: (1,9), (2,8), (3,7), (4,6)

Also, (5,5) can be considered as a rectangle (as every square is a special type of rectangle )

Thus, five rectangles can be formed with the given wire.

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