Chapter 11: Q27. (page 427)

A path2mwide surroundings a rectangular garden 20mlong and 12mwide. Find the area of the path.

Short Answer

Expert verified

The area of the path is $144 m^{2} .$

Step by step solution

Step 1. Given information.

Length of the garden $= 20 m$

Width of the garden $= 12 m$

Width of the path $= 2 m$

Step 2. Concept Used.

If b is the base of the reactangle and h is the height of the rectangle.

Then, the area of the rectangle is $A = b \times h$

Step 3. Let’s calculate the area of the path.

In $▱ P Q R S$ where,

Length= $(20 + 2 + 2) = 24 m$

Width= $(12 + 2 + 2) = 16 m$

Put the value of length and width into the formula and find the area.

Area of the $▱ P Q R S$ : $\begin{matrix} A_{1} = 24 \times 16 \\ = 384 m^{2} \end{matrix}$

Now, $▱ A B C D$

Inwhere,

Length= $20 m$

Width= $12 m$

Put the value of length and width into the formula and find the area.

Area of the $▱ A B C D$ :

$\begin{matrix} A_{2} = 20 \times 12 \\ = 240 m^{2} \end{matrix}$

Now,

The area of the path = Area of the rectangle PQRS-Area of the rectangle ABCD

$\begin{matrix} A = (384 - 240) \\ = 144 c m^{2} \end{matrix}$

Therefore, the area of the path is $144 c m^{2} .$

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A path2mwide surroundings a rectangular garden 20mlong and 12mwide. Find the area of the path.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Let’s calculate the area of the path.

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