InterviewSolution
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InterviewSolution
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Consider all rectangles that can be made with a 1-metre long rope. Take one of its sides as x centimetres and the area enclosed as a(x) square centimetres.i. Write the relation between a(x) and x as an equation.ii. Why are the numbers a(10) and a(40) equal?iii. To get the same number as a(x), for two different numbers as x, what must be the relation between the numbers? |
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Answer» i. 1 m = 100 cm If one side is x cm, then the other side is 50 – x. Area of rectangle = a(x) = x(50 – x) = 50x – x2 cm2 a(x) = 50x – x2 ii. a(10) = 50 × 10 – 102 = 500 – 100 = 400 a(40) = 50 × 40 – 402 = 2000 – 1600 = 400 10 and 40 are the sides of rectangle, so a(10) and a(40) are same . iii. Numbers must be sides of rectangle. If we add the two numbers together we get the sum as half the length of the wire (50 cm) used to make it. |
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