Mathematics
Grade-8
Easy

Question

A square garden has an area of 225 square feet.  How much fencing would a gardener need to buy to place it around the garden?

  1. 56.25 ft
  2. 112.5 ft
  3. 15 ft
  4. 60 ft

hintHint:

A square garden has an area of 225 square feet.  How much fencing would a gardener need to buy to place it around the garden?
In this question, we have given the square garden having an area of 225 square feet. The concept of square function or square root can be used here. A number's square root is a value that, when multiplied by itself, yields the original number. The other way to square an integer is to find its square root.
For example, take a number 144, then the square root of this will be:
square root of 144 equals 12

 

The correct answer is: 60 ft


    Here we have given that the garden is square, so all the sides will be same. Then we have given that the area of the square garden is 225 square feet. So here we can use the area of square formula.

    A r e a space o f space s q u a r e equals s i d e cross times s i d e
A r e a space o f space s q u a r e equals left parenthesis s i d e right parenthesis squared
N o w space w e space k n o w space t h e space a r e a space o f space s q u a r e space a s space 225 space s q u a r e space f e e t comma space s o space p u t t i n g space t h e space v a l u e space i n space t h e space f o r m u l a comma space w e space g e t colon
left parenthesis s i d e right parenthesis squared equals 225 space f t squared
T a k i n g space s q u a r e space r o o t space o n space b o t h space s i d e s comma space w e space g e t colon
square root of left parenthesis s i d e right parenthesis squared end root equals square root of 225 space f t squared end root
N o w space s i m p l i f y i n g space i t comma space w e space g e t colon
s i d e equals square root of 15 cross times 15 space f t squared end root
s i d e equals 15 space f t
S o space t h e space d i m e n s i o n space o f space o n e space s i d e space o f space f e n c i n g space w i l l space b e space 15 space f e e t.
N o w space t h e space q h o l e space d i m e n s i o n space o f space t h e space s q u a r e d space g a r d e n space w i l l space b e colon
F e n c i n g space o f space g a r d e n equals 4 cross times 15 space f e e t
F e n c i n g space o f space g a r d e n equals 60 space f e e t
S o space t h e space f e n c i n g space o f space t h e space s q u a r e d space g a r d e n space i s space 60 space f e e t.

    In this question, we have given that a square garden has an area of 225 square feet, and the dimension was supposed to be found. We used the concept of square root where the area was already given and with the help of that we calculated the dimension of fencing of one side and multiplied by 4 to get the total dimension of the squared garden which came out to be 60 feet.

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