Question

A rectangular Lown is
15m Long and Im wide
it has a path 1.5m
Wide all around it. Find the
area of the Path

Answer 1

Answer:

Imagine a square within a square.

Find the area of the path as if it were a square (pretend there’s no park in the middle) and then find the area of the park. subtract the two and you have the area of your path.

So your path square area would be 11m x 9m = 99m squared

Your park square area would be 10 x 8m = 80m squared

So your path’s total area is 99 minus 80 = 19m squared

Answer 2

Let the width of the path be x metres.

Length of the field including the path `=(20+2x)m.`

Breadth of the field including the path

`=(14+2x)m.`

Area of the field including the path `=(20+2x)(14+2x)m^(2).`

Area of the field excluding the path `=(20xx14)m^(2)=280m^(2).`

`:." "" the area of the path "=[(20+2x)(14+2x)-280]m^(2).`

`:." "(20+2x)(14+2x)-280=111`

`implies" "4x^(2)+68x-111=0implies4x^(2)+74x-6x-111=0`

`implies" "2x(2x+37)-3(2x+37)=0implies(2x+37)(2x-3)=0`

`implies" "x=-(37)/(2)" or "x=(3)/(2)`

`implies" "x=(3)/(2)=1.5" "[because" width can never be negative"]`,

Hence, the width of the path is 1.5 m.