Question

A regular field is 20m long and 14m wide there is path of equal width all around it .having an area 111sq.m find the width of the path

Answer 1

Answer:

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Answer 2

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Correct Question - A rectangular field is 20m long and 14m wide. There is a path of equal width all around it.having an area 111sq.m find the width of the path

Solution :-

Assumption,

Width = p m

Also

Length = 20 + 2p m

Width of path = 14 + 2p m

Situation,

As we know that

Area of rectangular path = L × B

= (20 + 2p)(14 + 2p)

= 4p² + 68p + 280

Given,

Area of path = 111 m²

So,

4p² + 68p + 280 = 111 m²

Subtract 280 from LHS, we get,

4p² + 68p + 280 - 280 = 111 m²

4p² + 68p = 111 m²

4p² + 68p - 111 = 0

4p² + 74p - 6p - 111 = 0

2p(2p + 37) - 3(2p + 37) = 0

(2p + 37)(2p - 3) = 0

p = -37/2, 3/2 = 0

p = -18.5, 1.5 (Negative value is not applicable)

p = 1.5 m

Therefore,

Width of path = 1.5 m