Question

There is a 2 metre wide road outer side a square garden if the area of the path is 9680 square metre. Find the area of the garden.
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Answer 1

$\Large\underline{\underline{\sf \blue{Given}:}}$

• Width of road = 2 mtr.
• area of the path = 9680 sq.mtr.

$\Large\underline{\underline{\sf \blue{To\:Find}:}}$

• Area of the garden ?

According to the attachment there are four equal rectangles.

$\implies$Area of rectangle = 9680 sq.mtr

$\implies$Area of these four rectangles =9680 sq.meter

$\implies$Area of 1 rectangle = $\sf\cancel\dfrac{9680}{4}$ =2420 sq.meter

$\implies$length of the rectangle =$\sf\cancel\dfrac{2420}{2}$= 1210 meter

$\implies$or length of the inner square =1210 - 2 =1208 meter.

$\implies$ $\therefore$Area of the garden=1208×1208

= 1,459,264 sq.mtr.

Answer 2

Given :----

• Area of path outside square garden = 9680m²
• width of path = 2m

To Find :-----

• Area of square garden ?

Formula used :----

• Area of square = side × side .

Solution :------

• Let side of square garden be = x metre .

Since 2m path is along all 4 sides of path, it will also make a square outside it..

side of outer square = side of square garden + 2(width of path)

side of outer square = x + 2×2 = (x+4) metre .

Now, Area of path = Area of outer square - Area of inner garden = 9680m²

so,

$(x + 4)^{2} - {x}^{2} = 9680 \\ \\ {x}^{2} + 16 + 8x - {x}^{2} = 9680 \\ \\ 8x = 9664\\ \\ x = 1208$

x = 1208m

So,

Area of square garden = (1208)² = 1459264m² (Ans)

(Hope it helps you)