A footpath of uniform width runs all around the inside of a rectangular field long and 38m wide. If the area of the path is , Find the width ?

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2 m

15 m

3 m

41 m

answer is C.

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Detailed Solution

Concept- In this question, we will use the concept of a rectangle to find the width of the sidewalk. Therefore, consider the width variable and the area of the path in the question is the area of the rectangle in the sidewalk. It is subtracted from the total area of the rectangular field. Associates a given area with a base area. This leads to a quadratic equation. Thanks to that, you can solve the equation and get the required width.
First, for a better understanding, create a rectangular field and sidewalk diagram. Question Image

Let the rectangle be from ABCD. Where AB is the width of the rectangle, And AD will be rectangular in length, The width of the sidewalk is x m Next, you need to find the length and width of the rectangular sidewalk. The length of the smaller rectangle is = the length of the rectangle ABCD-2 times Sidewalk width (because the sidewalk surrounds the smaller rectangle) ABCD = 50 m as the length of the rectangle The width of the sidewalk is x m. Therefore, the length of the smaller rectangle is =

m resemble, The width of the smaller rectangle is equal to the width of the rectangle ABCD-2 times Sidewalk width (because the sidewalk surrounds the smaller rectangle) ABCD = 38 m as the width of the rectangle The width of the sidewalk is x m. Therefore, the width of the smaller rectangle is

m
Total area of rectangle = area of footpath + remaining part