Question

A footpath of uniform width runs all around the inside of a rectangular field 50m long and 38m wide. if the area of the path is 492msq find its width ​

Answer 1

★Given:-

• A footpath of uniform width runs all around the inside of a rectangular field.
• Length of rectangular field = 50m
• Width of rectangular field = 38m
• Area of the path = 492m²

★To find:-

• Width of the path.

★Solution:-

Let the width of footpath is x.

Using the formula,

✦Area of rectangle = length×breadth

Total area of rectangle:-

➜l×b

➜50×38

➜1900

Area of remaining part:-

➜l×b

➜(50-2x)×(38-2x)

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

➜50×38 = 492+[(50-2x)×(38-2x)]

➜1900=492+[1900-100x-176x+4x²]

➜4x²-176x+492=0

➜x²- 44x+123=0

➜(x-3)(x-41)=0

➜x-3 = 0 (or) x-41=0

➜x=3  (or) x=41

But x = 41 is not possible.

∴x=3m

Hence,its width is 3m.

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