Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The area of a 6m wide road outside a garden in all its four is 564 sq meters. If the length of the garden is 20m, what is its breadth?A) 15 mB) 20 mC) 25 mD) 30 m

Last updated date: 20th Jun 2024
Total views: 414.3k
Views today: 5.14k
Verified
414.3k+ views
Hint: An area is the size of a two-dimensional surface. The area of a rectangle is the space contained within a set of lines. To find out the area of a rectangle border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.

This gives details of a road around a garden – the path is 6m wide.
Let breadth of garden be x meters.
Length of garden=20 m
We can work out the dimensions of the outer section because we know the path around the edge is 6m wide.
Now the new length of a garden with road = 20 + 6 + 6 = 32 m
Now the new breadth of a garden with road = x + 6 + 6 = (x + 12) m
To find out the area of a rectangle border, we need to subtract the area of the inner rectangle from the area of the outer rectangle.
Given, the area of the road = 564 sq meters
Now, area of road= Area of the outer rectangle – area of the inner rectangle
$\Rightarrow 32(x + 12) - 20x = 564 \\ \Rightarrow 32x + 384 - 20x = 564 \\ \Rightarrow 12x = 564 - 384 = 180 \\ \Rightarrow x = 15 \\$