A rectangular garden is 20 m by 25m. It is surrounded by a sidewalk. The outside perimeter of the sidewalk is 114m. What is the width of the sidewalk?
let the width of the sidewalk be x m
new dimensions:
20+2x by 25+2x
2(20+2x) + 2(25+x) = 114
40 + 4x + 50 + 4x = 114
8x = 24
x = 3
the sidewalk is 3 m wide.
To find the width of the sidewalk, we first need to calculate the length and width of the rectangular garden including the sidewalk.
Let's assume the width of the sidewalk is 'x'.
So, the length of the garden including the sidewalk would be 20m + 2*x (since the garden has a sidewalk on both the sides).
Similarly, the width of the garden including the sidewalk would be 25m + 2*x (since the garden has a sidewalk on both the sides).
Now, the outside perimeter of the sidewalk is given as 114m.
Perimeter = 2*(Length + Width)
So, 114 = 2*(20 + 2*x + 25 + 2*x)
Simplifying the equation, we get:
114 = 90 + 4*x
Now, let's solve for 'x':
4*x = 114 - 90
4*x = 24
x = 24/4
x = 6
Therefore, the width of the sidewalk is 6 meters.