Question

A rectangular field is 50 m long and 40 m wide. There is a path of uniform width all
around inside it. If the area of the path is 800 m², find its width.
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Answer 1

Answer:

This is the answer i hope this may help u.

Answer 2

Step-by-step explanation:

Let the width of the path be ' x m '.

So, Length of inside rectangle = 50-2x

And, Breadth of inside rectangle = 40-2x

Also, Area of inside rectangle = length × breadth = [(50−2x)×(40−2x)]

Total Area of rectangular field = Area of path + Area of inside rectangle

=> 50×40= 800+[(50−2x)×(40−2x)]

=> 2000 m^2 = 800+[2000-100x-80x+4x^2]

=> 2000 m^2 = 800+[2000-180x+4x^2]

=> 2000 m^2 = 800 + 2000 - 180x + 4x^2

=> 2000 m^2 = 2800 - 180x + 4x^2

=> 2800 - 180x + 4x^2 - 2000 = 0

=> 800 - 180x + 4x^2 = 0

=> 4(x^2 - 45x + 200) = 0

=> 4(x^2 - 5x - 40x + 200) = 0

=> 4[x(x-5)-40(x-5)] = 0

=> 4(x-5) × (x-40) = 0

=> (x-5)×(x-40) = 0 { Dividing both sides by 4}

Now, By Solving the 1st equation for x, we will get the width of the path :-

x-5 = 0

Therefore, x = 5

So, the width of the path = 5m.

Hope it helps :)