Question

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.

Answer 1

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`