Question

All round outside of a square garden there is a path 1 m wide. If the area of the path is 324 sq. m then what is the area of the garden?​

Answer 1

Answer:

6400 square meters.

Step-by-step explanation:

let length of square be x

then, area of square garden is x^2.

Area of the square garden + the 1m wide path= (x+2)^2

so, we have:

Area of 1m wide path:

(x+2)^2 - x^2= 324

expand and simplify

x^2+4x+4-x^2=324

4x+4=324

4x=324-4

x=320/4

x= 80

So, area of the garden=x^2=80*80=6400 square meters.

Ans: Area of the square garden is 6400 square meter.

Answer 2

Answer:

6400m^2

Step-by-step explanation:

Let side of the square garden= 'a' metre.

So, area of the square garden= 'a^2' m^2.

Including path,

side of garden= [a+(1+1)]m = (a+2)m.

& area of garden= (a+2)^2 m^2.

Therefore, A.T.P,

(a+2)^2 – a^2 = 324

=> a^2+ 2×a×2 + 4 – a^2 = 324

=> 4a + 4 = 324

=> 4a = 324 – 4

=> 4a = 320

=> a = 320/4

=> a = 80

Hence, original side of the garden is 80m.

Thus, area of the square garden= (80)^2 = 6400m^2.