A footpath of uniform width 5 m runs on the outside of a rectangular field of 40m by 32m. Find the area of the path. Also find the cost of construction of the path at 50 paise per square metre.
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A footpath of uniform width runs all around the inside of rectangular field 50m long and 38m wide.If the area of the path is 492m
2
,find its width ?
Medium
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Let the width of footpath=x
total area of rectangle ABCD = area of footpath + area of EFGH
⇒50×38=492+[(50−2x)×(38−2x)]
⇒1900=492+[1900−100x−176x+4x
2
]
⇒4x
2
−176x+492=0
⇒x
2
−44x+123=0
⇒(x−3)(x−41)=0
∴x=3m
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footpath of uniform width 5 m runs on the outside of a rectangular field of 40m by 32m. Find the area of the path. Also find the cost of construction of the path at 50 paise per square metre.
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