CBSE Class 7 Mathematics Chapter 11: Perimeter and Area - NCERT Solutions

We are given the dimensions of a rectangular piece of land:

• Length = 500 m
• Breadth = 300 m

1. To find the area:

The formula for the area of a rectangle is Length × Breadth.

$$Area\; =\; 500\; \backslash text\{\; m\}\; \backslash times\; 300\; \backslash text\{\; m\}$$

$$Area\; =\; 1,50,000\; \backslash text\{\; m\}^2$$

So, the area of the rectangular piece of land is 1,50,000 square meters.

2. To find the cost of the land:

We are given that the cost of 1 square meter of land is ₹10,000.

To find the total cost, we multiply the total area by the cost per square meter.

$$Total\; Cost\; =\; Area\; \backslash times\; \backslash text\{Cost\; per\; m\}^2$$

$$Total\; Cost\; =\; 1,50,000\; \backslash text\{\; m\}^2\; \backslash times\; ₹10,000\; /\; \backslash text\{m\}^2$$

$$Total\; Cost\; =\; ₹1,50,00,00,000$$

Therefore, the cost of the land is ₹1,50,00,00,000 (one hundred fifty crore rupees).

We are given the perimeter of a square park:

Perimeter = 320 m

The formula for the perimeter of a square is $P\; =\; 4\; \backslash times\; side$.

We can use this to find the length of one side:

$$4\; \backslash times\; side\; =\; 320\; \backslash text\{\; m\}$$

To find the side, we divide the perimeter by 4:

$$side\; =\; \backslash frac\{320\; \backslash text\{\; m\}\}\{4\}$$

$$side\; =\; 80\; \backslash text\{\; m\}$$

Now that we have the side length, we can find the area of the square park.

The formula for the area of a square is $Area\; =\; side\; \backslash times\; side$.

$$Area\; =\; 80\; \backslash text\{\; m\}\; \backslash times\; 80\; \backslash text\{\; m\}$$

$$Area\; =\; 6400\; \backslash text\{\; m\}^2$$

Thus, the area of the square park is 6400 square meters.

We are given the area and length of a rectangular plot:

• Area = 440 m²
• Length = 22 m

The formula for the area of a rectangle is $Area\; =\; Length\; \backslash times\; Breadth$.

We can rearrange this formula to find the breadth:

$$Breadth\; =\; \backslash frac\{Area\}\{Length\}$$

Substituting the given values:

$$Breadth\; =\; \backslash frac\{440\; \backslash text\{\; m\}^2\}\{22\; \backslash text\{\; m\}\}$$

$$Breadth\; =\; 20\; \backslash text\{\; m\}$$

So, the breadth of the rectangular plot is 20 meters.

Now, we need to find the perimeter of the rectangular plot.

The formula for the perimeter of a rectangle is $Perimeter\; =\; 2\; \backslash times\; (Length\; +\; Breadth)$.

Using the given length and the calculated breadth:

$$Perimeter\; =\; 2\; \backslash times\; (22\; \backslash text\{\; m\}\; +\; 20\; \backslash text\{\; m\})$$

$$Perimeter\; =\; 2\; \backslash times\; (42\; \backslash text\{\; m\})$$

$$Perimeter\; =\; 84\; \backslash text\{\; m\}$$

Thus, the breadth of the rectangular plot is 20 m and its perimeter is 84 m.

We are given the perimeter and length of a rectangular sheet:

• Perimeter = 100 cm
• Length = 35 cm

The formula for the perimeter of a rectangle is $P\; =\; 2\; \backslash times\; (Length\; +\; Breadth)$.

We can use this to find the breadth:

$$100\; \backslash text\{\; cm\}\; =\; 2\; \backslash times\; (35\; \backslash text\{\; cm\}\; +\; Breadth)$$

First, divide both sides by 2:

$$\backslash frac\{100\; \backslash text\{\; cm\}\}\{2\}\; =\; 35\; \backslash text\{\; cm\}\; +\; Breadth$$

$$50\; \backslash text\{\; cm\}\; =\; 35\; \backslash text\{\; cm\}\; +\; Breadth$$

Now, subtract the length from this value to find the breadth:

$$Breadth\; =\; 50\; \backslash text\{\; cm\}\; -\; 35\; \backslash text\{\; cm\}$$

$$Breadth\; =\; 15\; \backslash text\{\; cm\}$$

So, the breadth of the rectangular sheet is 15 cm.

Next, we need to find the area of the rectangular sheet.

The formula for the area of a rectangle is $Area\; =\; Length\; \backslash times\; Breadth$.

Using the given length and the calculated breadth:

$$Area\; =\; 35\; \backslash text\{\; cm\}\; \backslash times\; 15\; \backslash text\{\; cm\}$$

$$Area\; =\; 525\; \backslash text\{\; cm\}^2$$

Thus, the breadth of the rectangular sheet is 15 cm and its area is 525 cm².

We are given that the area of a square park is equal to the area of a rectangular park.

Details of the square park:

• Side = 60 m

Details of the rectangular park:

• Length = 90 m
• Breadth = ?

First, let's calculate the area of the square park:

$$Area\; of\; Square\; =\; side\; \backslash times\; side$$

$$Area\; of\; Square\; =\; 60\; \backslash text\{\; m\}\; \backslash times\; 60\; \backslash text\{\; m\}$$

$$Area\; of\; Square\; =\; 3600\; \backslash text\{\; m\}^2$$

Since the area of the rectangular park is the same as the area of the square park, the area of the rectangular park is also 3600 m².

Now, we use the formula for the area of a rectangle: $Area\; =\; Length\; \backslash times\; Breadth$.

We can rearrange this to find the breadth:

$$Breadth\; =\; \backslash frac\{Area\}\{Length\}$$

Substitute the known values:

$$Breadth\; =\; \backslash frac\{3600\; \backslash text\{\; m\}^2\}\{90\; \backslash text\{\; m\}\}$$

$$Breadth\; =\; 40\; \backslash text\{\; m\}$$

Thus, the breadth of the rectangular park is 40 meters.