Home
Class 9
MATHS
Consider all rectangles that can be made...

Consider all rectangles that can be made with a 1m long rope. Take one of its side as x cm and the area enclosed as a(x) sq.cm.
i) Write the relation between a(x) and xas in 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?

Text Solution

Verified by Experts

i) 1m =100cm
If length of one side is x cm, then length of other side is 50-x cm
a(x)= x(50-x)
ii) a(10)=400
a(40)=400
Promotional Banner

Topper's Solved these Questions

  • Parallel Lines

    V PUBLICATION|Exercise QUESTION BANK|49 Videos

  • PRISMS

    V PUBLICATION|Exercise QUESTIONBANK|65 Videos

Similar Questions

Explore conceptually related problems

In rectangle with one side 1cm shorter than the other , take the length of the shorter side as x cm. i) Taking their perimeters as p(x) cm, write the relation between p(x) and x as an equation. ii) Taking their areas as a(x) sq.cm, write the relation between a(x) and x as an equation. iii) Calculate p(1),p(2),p(3),p(4),p(5). Do you see any pattern? iv) Calculate a(1),a(2),a(3),a(4),a(5).Do you see any pattern?

Consider two consecutive odd natural numbers both of which are larger than 10, such that their sum is less than 40. If the first odd natural numbers is x, what will be the other odd natural numbers?

A rope of length 40 metres is cut into two pieces and two squares are made on the floor with them. The sum of the. area enclosed is 58 square meter. a) If the length of one piecce is taken as 'x', what is the. length of the other piece. b) What are the lengths of the sides of the squares? c) Write the. given fact about area as an algebraic equation. d) What is the length of each piece?

From the four corners of a rectangle, small squares are cut off and the sides are folded up to make a box, as shown below:(fig) i) Taking a side of the square as x cm, write the dimensions of the boxin terms of x. ii) Taking the volume of the box as v(x) cubic cm, write the relation between v(x) and x as an equation.

Consider the polynomial p(x)=a x^3-x^2-b x-1 a) Find 'p ( 1 )' b) What is the relation between a and 'b' if 'x-1' is a factor of 'p(x) ?' c) What is the relation between a and b if 'x+1' is a factor of 'p(x) ?' d) Will 'p(x)' have both '(x+1)' and '(x-1)' as a factors for any number a and b? Justify.

Identify the quantifier in the following statements and write the negation of the statements. i) There exists a number which is equal to its square. ii) For every real number x , x is less than x+1 iii) There exists a capital for every state in India

All the terms of an arithmetic sequence with common difference 4 are positive numbers. The. product of two consecutive terms of this sequence is the same as their sum. i) If one term is 'x', what is the next term? ii) Calculate those terms.

"One mole of all substances contain the same number of specified particles". a. Justify the statement. b. How to connect mole, gram atom and gram mole? c. What is the relation between mole and volume? d. Calculate the number of mole of a gas in i. 44.828L at STP ii. 11.207ml at STP

V PUBLICATION-POLYNOMIALS-Question Bank
  1. In rectangle with one side 1cm shorter than the other , take the lengt...

    Text Solution

    |

  2. From the four corners of a rectangle, small squares are cut off and th...

    Text Solution

    |

  3. Consider all rectangles that can be made with a 1m long rope. Take one...

    Text Solution

    |

  4. Write each of the relations below in algebra and see if it gives a pol...

    Text Solution

    |

  5. Write each of the operations below as algebraic expressions, find out ...

    Text Solution

    |

  6. Find p(1) and p(10) in the following polynomials. i) p(x)= 2x+5 ii) ...

    Text Solution

    |

  7. Find p(0), p(1) and p(-1) in the following polynomials. i) p(x)= 3x+6 ...

    Text Solution

    |

  8. Find polynomial p(x) satisfying each set of conditions below. i) Firs...

    Text Solution

    |

  9. Write down the algebraic expression to find out each of the following....

    Text Solution

    |

  10. What is the algebraic expression denoting the hypotenuse of a right an...

    Text Solution

    |

  11. The area of a rectangle is 50 sq.cm. Write down the algebraic express...

    Text Solution

    |

  12. For p(x)= 2 x^ 2 − 3 x + 1 , find p(0),p(1),p(-1)

    Text Solution

    |

  13. If p(x)= 3 x^ 2 − a x + 1 and we want p(1) =2 what number should we ta...

    Text Solution

    |

  14. If p(x)= 2 x^ 3 + a x^ 2 − 7 x + b and we want p(1)=3 and p(2)=19 wha...

    Text Solution

    |

  15. A ball is thrown upwards with a speed of 40m/cm loses speed at the rat...

    Text Solution

    |

  16. In the polynomial p(x)= 2 x^ 3 − 3 x^ 2 − 11 x − 6 find p(3),p(-2) a...

    Text Solution

    |

  17. For p(x)= ax^3 + b x^2 + c x + d .If p(1)=p(-1) prove that a+c=0

    Text Solution

    |

  18. a)If p(x) =4x-4, find the numbers p(1) and p(2). b) Write a first degr...

    Text Solution

    |

  19. 100xx17=1700,isn't it? So, when 1700 is divided by 100 will get quotie...

    Text Solution

    |

  20. The expression given below, which of them are polynomials. i) x^ 3 + ...

    Text Solution

    |