Question

A rectangular garden is of length 50 m and breadth 30 m. A path of 3.5 m is made inside along the boundary of garden. Find the area of the path.​

Answer 1

Answer :-

Area of the path = 511 m²

$\rule{150}2$

Given:-

• A rectangular garden is of length 50 m and breadth 30 m.
• A path of 3.5 m is made inside along the boundary of garden. (width = 3.5 m)

Find:-

Area of the path.

Solution:-

Area of rectangle = length × breadth

$\implies$ 50 × 30

$\implies$ 1500 m²

Also, a path of 3.5 m is made inside the rectangular path.

Now,

New length of rectangular park = 30 - 2(3.5)

⇒ 30 - 7

⇒ 23 m

A new breath of rectangular park = 50 - 2(3.5)

⇒ 50 - 7

⇒ 43 m

Now, we have -

• length of rectangular park = 23 m
• breadth of rectangular park = 43 m

Area of rectangle = length × breadth

$\implies$ 23 × 43

$\implies$ 989 m²

So,

Area of path = Area of the rectangular park - Area of the rectangular park when width is 3.5 m

⇒ 1500 - 989

⇒ 511 m²

Answer 2

$\LARGE\underline{\underline{\sf Given:}}$

• Length of garden = 50m

• Breadth of garden = 30m

• Path = 3.5m inside

$\LARGE\underline{\underline{\sf To\:Find:}}$

• Area of path (A) = ?

$\LARGE\underline{\underline{\sf Solution:}}$

Area of Original Garden :-

$\large\implies{\sf 50×30 }$

$\large\implies{\sf1500m^2 }$

Since ,

Width is = 3.5m

Length (PR) $\implies{\sf 30-2(3.5) }$

$\large\implies{\sf 30-7}$

$\large\implies{\sf 43m }$

Similarly ,

Length (QR) $\implies{\sf 50-2(3.5) }$

$\large\implies{\sf 50-7 }$

$\large\implies{\sf 43m }$

Area (PQRS) : Length × Breadth

$\large\implies{\sf 23×43}$

$\large\implies{\sf 989m^2 }$

Area of path = Area(ABCD) - Area(PQRS)

$\large\implies{\sf 1500-989 }$

$\large\implies{\sf 511m^2}$

$\LARGE\underline{\underline{\sf Answer:}}$

•°• Area of path is 511m²