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The frame will have a solid base and will be cut out of a piece of steel the final area of the frame should be 54 sq m. The diagram of frame is shown below. Inner rectangle dimensions are l-10 b-5. Outer is xmeters from all sides. What are the dimensions of the outer frame? (a) (10+x)and(5+x)(b) (10-x)and(5-x)(c) (10 +2x) and (5 + 2x)(d) (10-2x)and(5-2x)(i)1(ii)A metal sheet of minimum area is used to make the frame. What should be the minimum area of metal sheet before cutting?(a) 4x2 + 30x + 50. (b)x2 +27x+55. (c) 5x2 + 30.(d) 4x2 +50.1(iii)What is the area of required final metal frame? (a) 4x2 + 30x +50 m2.(b) x2 + 27x +55 m2.(c) 4x2 +50x m2.(d) 4x2 + 30x m2.(iv)If the area of the frame is 54 sq m, what is the value of x ? (a) 0.75 m(b) 3.0 m (c) 1.5 m (d) 1.8 m |
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Answer» Given : final area of the FRAME should be 54 sq m Inner rectangle dimensions are l-10 b-5. Outer is x meters from all sides To Find : dimensions of the outer frame Solution: dimensions of the outer frame 10 + x + x and 5 + x + x = 10 + 2x and 5 + 2x Correct option is : c) (10 +2x) and (5 + 2x) Area of frame = (10 +2x)(5 + 2x) = 50 + 20x + 10x + 4x² = 4x² + 30x + 50 area of required final metal frame = 4x² + 30x + 50 - ( 10 * 5) = 4x² + 30x 4x² + 30x = 54 => 2x² +15x = 27 => 2x² +15x - 27 = 0 => 2x² + 18x - 3x - 27 = 0 => 2x(x + 9) - 3(x + 9) = 0 => (2x - 3)(x + 9) = 0 => x = 3/2 x = - 9 ( x can not be negative ) Hence x = 1.5 m Learn More: The outer length and breadth of a photo frame is 60 cm × 40 cm.If . |
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