A foot path of uniform width runs all around the inside of a rectangular field 50 m long and 38m wide. If the area of the path is 492 m². Find its width.
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Answered by
1
Step-by-step explanation:
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+4x2]
⇒4x2−176x+492=0⇒x2−44x+123=0
⇒(x−3)(x−41)=0
∴x=3m
Answered by
1
Answer:
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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