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A carpet is laid on the floor of a room 8 m by 5 m. There is a border of constant width all around the carpet. If the area of the border is 12 m²,find its widthde cach 5 m wide, running |
| Answer» LET the width of the BORDER is 'x' m. And The length and breadth of the carpet are 8 m and 5 MAREA of the carpet = 8m×5m = 40m²length of the carpet without border = (8 – 2X) breath of the carpet without border = (5–2x)area of the border is 12m²area of the carpet without border (8–2x)(5–2x)Thus ,12= 40– (8–2x)(5–2x) ==>12= 40-(40-26x +4x²)==>12= 26x - 4x²==>26x 4x²= 12Then, ==>4x² – 26x +12= 0 ==>2x²– 13x +6= 0 ==>(2x - 1)(x-6) = 0 ==>2x - 1= 0 and x - 6 = 0 ==> x = 1/2 and x = 6Because the border cannot be WIDER than the entire carpet, the width of the carpet is 1/2 m i.e., 50 cm. | |