Question

A square garden has a 2 m wide path surrounding it. If the area of the path is
136 m 2, find the area of the garden

Answer 1

Here is your answer friend,

Let the side of the Square garden be X

therefore the area of the Square garden will be,

${x}^{2}$

$(area = {side}^{2} )$

And then,

we can observe from the figure that the side of the larger square(square including the path) will be X+4

And from the figure we can see that the area of the path = area of larger square - area of smaller one.

so on substituting it we get,

${(x + 4)}^{2} - {x}^{2} = 136$

(136 is given.i.e area of path)

so we get,

${x}^{2} + 8x + 16 - {x}^{2} = 136$

and both the X2 will cancel out, so

$8x + 16 = 136$

$8x = 120$

and so,

$x = 120 \div 8$

that is,

$x = 15$

that means we got the side of the garden that is X = 15m

so to find the area we get,

$area = {x}^{2} = {15}^{2} = 225 {m}^{2}$

HOPE YOU GOT IT,

THIS IS MY 100TH ANSWER..