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)
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(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.
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(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
Answers
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
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The outer length and breadth of a photo frame is 60 cm × 40 cm.If .
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i)c)(10+2x)and(5+2x)
ii)a)4x^2+30x+50
iii)d)4x^2+30x m^2
iv)c)1.5m