Question

A wire of 20m is to be folded in the form of rectangle. how many rectangie can be made by folding the wire if the sides are positive integers in meters

Answer 1

Answer:

Dear Student!

Length of the wire = 20 m

Let the length and breadth of the rectangle be l and b respectively.

Perimeter of the rectangle = Length of the wire

∴ 2(l + b) = 20 m

⇒ l + b = 10 m

When l = 9 m, b = 10 – 9 = 1 m

When l = 8 m, b = 10 – 8 = 2 m

When l = 7 m, b = 10 – 7 = 3 m

When l = 6 m, b = 10 – 6 = 4 m

When l = 5 m, b = 10 – 5 = 5 m

When the lengths of the rectangle are taken as 6m, 7m, 8m and 9m, then the breadth of the rectangle are 4m, 3m, 2m and 1m respectively. But, the rectangle of these measurement have been obtained earlier.

Thus, 5 rectangles can be formed by folding the wires, if the sides of the rectangle are positive integers.

Cheers!

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

AnswEr:

• Five rectangles can be formed with the given wire.

Given Information:

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

Need To Find:

• How many rectangles can be formed with the given wire = ?

ExPlanation:

Perimeter of the rectangle = 20 m [Given]

⇒ 2(Length + Breadth) = 20 m

⇒ (Length + Breadth ) = 20/2 = 10 m

Since,

• Length and Breadth are positive integers in metres,

ThereFore:

The possible dimensions are:

• (1m, 9m), (2m, 8m), (3m, 7m), (4m, 6m) and (5m, 5m)

Hence:

• Five rectangles can be formed with the given wire.

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What is Perimeter?

• The length of the boundary of a closed figure is called the perimeter.

• Perimeter of rectangle = 2 × (Length + Breadth)
• Perimeter of a square = 4 × Side

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