Question

A rectangular field with 40 m length and 30 m breadth has a path around it with an area of 144 m². Find the width of the path.​

Answer 1

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

Easy

Solution

Let width of path x

Length =20+2x

Width =14+2x

Area of outer rectangular =l×b

=(20+2x)(14+2x)

=4x

2

+68x+280

Area of path:

4x

2

+68x+280−280=111

4x

2

+68x=111

4x

2

+68x−111=0

(4x

2

+74x−6x−111)=0

(2x−3)(2x+37)=0

x=

2

3

m or x=−

2

37

Since, width can not be −ve

Hence, the width is 1.5 m

Step-by-step explanation:

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