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प्रश्न
A carpet is laid on floor of a room 8 m by 5 m. There is border of constant width all around the carpet. If the area of the border is `12m^2` find its width.
उत्तर
Let the width of the border be x m.
The length and breadth of the carpet are 8 m and 5 m, respectively. Area of the carpet=`8xx5=40m^2`
Length of the carpet without border=`(8-2x)`
Breadth of carpet without border=`(5-2x)`
Area of the border`12m^2`
Area of the carpet without border=`(8-2x)(5-2x)`
Thus, we have:
`12=40-[(8-2x)(5-2x)]`
⇒ `12=40-(40-26x+4x^2)`
⇒ `12=26x-4x^2`
⇒ `26x-4x^2=12`
⇒`4x^2-26x+12=0`
⇒`2x^2-13x+6=0`
⇒`(2x-1)(x-6)=0`
⇒`2x-1=0 and x-6=0`
⇒`x=1/2 and x=6`
Because the border cannot be wider than the entire carpet, the width of the carpet is `1/2 m `
i.e. `50 cm`
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