Question

the square lawn is surrounded by a path 2.5 M wide if the area of the path is 165 CM square find the area of the lawn

Answer 1

let the side of the lawn be =x cm

the side of lawn with the path = x+5 cm

the area of small square lawn is = xto the power two [as area of square is                              

side square]

the area of lawn with the path=(x+5)2

the area of the path = area of bigger square - area of only lawn

165cm2=(x+5)2 -x2

165=25+10x

165-25=10x

140=10x

x=14

so the side of the lawn is 14 cm . so the area of the lawn without the path is 14 to the power 2 that is 196 .

but including the path the area becomes (14+5)to the power 2 i.e. 361cm square.