Question

A rectangular field is 25m long and 16 m broad . There is a path around it of equal breadth whose area is 148 square m. Find the breadth of the path.

Answer 1

then solve for the value of x find the value of x and then put in the new length

Answer 2

The breadth of the path is either 18.5 or 2.

Step-by-step explanation:

Area of a rectangle is

$Area= length\times breadth$

A rectangular field is 25m long and 16 m broad . Area of field is

$Area= 25\times 16=400$

There is a path around it of equal breadth whose area is 148 square m.

Let the breadth of the path we x.

Length = 25-2x

Breadth = 16-2x

Area of field without path = (25-2x)(16-2x)

Area of path Area of field - Area of field without path

$148=400-(25-2x)(16-2x)$

$148=400-[4x^2-82x+400]$

$148=400-4x^2+82x-400$

$148=-4x^2+82x$

$4x^2-82x+148=0$

$2(2x^2-41x+74)=0$

$2(2x^2-41x+74)=0$

Splitting the middle term we get

$2(2x^2-37x-4x+74)=0$

$2[x(2x-37)-2(2x-37)]=0$

$2(2x-37)(x-2)=0$

Using zero product property we get

$2x-37=0\Rightarrow x=18.5$

$x-2=0\Rightarrow x=2$

Therefore, the breadth of the path is either 18.5 or 2.

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