A playground which is 250 m long and 20 m broad is to be fenced with wire, then find how much wire is needed

A rectangle is a two-dimensional geometrical figure comprised of four sides, out of which opposite two sides are equal and parallel to each other. All the angles of the rectangle are equivalent to right angles. 

Properties of rectangle

• The opposite sides of a rectangle are equal.
• The diagonals are equal.
• All the four angles of a rectangle are equal.
• The diagonals of a rectangle bisect its angles.

Perimeter of a rectangle

The perimeter of a rectangle is referred to as the total length of the boundary enclosing the geometrical figure.

Perimeter of rectangle = Sum of all sides of a rectangle

Let us assume l to be the length of the rectangle and w to be its corresponding width. 

Since, we know, opposite sides of the rectangle are equal. 

Perimeter of rectangle = l + w + l + w

= 2l + 2w 

= 2(l + w)

A playground which is 250 m long and 20 m broad is to be fenced with wire, then find how much wire is needed.

Solution: 

A playground that is 250 m long and 20 m broad can be considered as a rectangle. The wire needed to fence the playground implies covering the boundaries of the playground with wire.

Let us assume the perimeter of rectangle to be given by P. 

Now, we have, 

l = 250 m

w = 20 m 

According to the formula, we have, 

P =  2(l + w)

Substituting the values, we get, 

P = 2(250 + 20)

= 2 (270)

= 540 m 

Therefore, the total wire required to fence the playground is equivalent to 540 m. 

Sample Questions

Question 1: Find the wire needed for fencing a rectangular stadium 500 m long and 100 m broad?

Solution:

Here we need to find the wire needed for fencing the rectangular stadium.

To find the wire needed for fencing we need to find the perimeter of the stadium.

As we know that

Perimeter of rectangle = 2 × (Length + Breadth)

Given :  

Length = 500 m

Breadth = 100 m

Perimeter of rectangle = 2 × (500 + 100)

Perimeter of rectangle = 2 × 600

Perimeter of rectangle = 1200 m

Wire needed for fencing the stadium will be 1200 m.

Question 2: Calculate which ground will require more wire for fencing; a square ground of side 150 m or a rectangular ground with length 150 m and breadth 50 m?

Solution:

Here we need to find which ground will require more wire

To find the wire needed for fencing we need to find the perimeter of both the ground.

As we know that

Perimeter of rectangle = 2 × (Length + Breadth)

Given :  

Length = 150 m

Breadth = 50 m

Perimeter of rectangular ground = 2 × (150 + 50)

Perimeter of rectangular ground = 2 × 200

Perimeter of rectangular ground = 400 m

Perimeter of square = 4 × Side

Given : Side = 150 m

Perimeter of square ground = 4 × 150

Perimeter of square ground= 600 m

Therefore,

Perimeter of square ground > Perimeter of rectangular ground.

Thus, 

Square ground will require more wire than Rectangular ground.

Question 3: Find the cost of fencing a rectangular plot of length 100 m and breadth 50 m at the rate of ₹50 per metre?

Solution:

Here we need of find the cost of fencing a rectangular plot

As we know that

Perimeter of rectangle = 2 × (Length + Breadth)

Given:

Length = 100 m

Breadth = 50 m

Perimeter of rectangle plot = 2 × (100 + 50)

Perimeter of rectangle = 2 × 150

Perimeter of rectangle = 300 m

To find cost of fencing multiply cost of fencing by perimeter 

Cost of fencing = ₹50 × 300

Cost of fencing = ₹15000.

Therefore,

Cost of fencing the rectangular plot is ₹15000.

Question 4: Calculate the cost of carpeting a rectangular yoga ground of length 50 m and breadth 25 m at the cost of ₹100 per m²?

Solution:

Here we have to find the cost of carpeting the yoga ground

To find the cost of yoga ground we need to multiply the cost of per m² to the area of the ground.

Area of rectangle = Length × Breadth

Given :

Length = 50 m

Breadth = 25 m

Area of rectangular yoga ground = 50 × 25

Area of rectangular yoga ground = 1250 m²

Now,

Find the cost of carpeting

Cost of carpeting = ₹100 × 1250

Cost of carpeting = ₹125000

Therefore,

Cost of carpeting the yoga ground is ₹125000.