Question

a feild is 70m long and 40 m broad .a path of uniform width runs all around inside the feild and covers an area of 1000msquare.find the width of the path .​

Answer 1

Answer:

Let us draw the diagram first to understand it better ✓

The diagram is in the attachment

$\huge{ \bold{explanation \: }}$

We have taken a rectangular park and named as ABCD✓

And a uniform path inside it with area = 1000m²

And the remaining portion inside the park is named PQRS

We have the dimensions of the rectangular park

$\red{length = 70m} \\ \red{breadth = 40m}$

So the area of the park is as follows

$\bold{length \times breadth = area} \\ area = 70 \times 40 = 2800m ^{2}$

$\therefore {area \: of \: the \: remaining \: portion \: PQRS \: = area \: of \: rectangular \: park - area \: of \: path}$

Area of PQRS = 2800-1000=1800m²

Now, let TS and RM be X m

So ,SR = (70-2x)m and QR= (40-2x)m

•°• Area of the portion PQRS is as follows

$area \: of \ \: PQRS\: = SR \times QR \: \: \\ \\ \ = > 1800 = (70 - 2x)(40 - 2x) \\ \\ = > 1800 = 2800 - 140x - 80x + 4x ^{2} \\ \\ > 4x ^{2} - 220x = - 1000 \\ \\ = > 4x ^{2} - 220x + 1000 = 0$

Now divide the equation by the cofficient of X²

So,

$= > x ^{2} - 55x + 250 = 0$

We need to do middle term so

$= > x ^{2} - 50x - 5x + 250 = 0 \\ \\ = > x(x - 50) - 5(x - 50) = 0 \\ \\ = > (x - 50)(x - 5) = 0$

$\green{either \: x = 50 \: or \: x = 5}$

So if X= 50 then breadth of the path is 50 m or if X= 5 then breadth = 5 m