Home
Class 9
MATHS
In rectangle with one side 1cm shorter t...

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?

Text Solution

Verified by Experts

If length of the shorter side is x cm, then length of the longer side is x+1 cm.
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

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 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?

p(x)= ax^2+bx+5 :- If (x+1) is a factor of p(x),then find the relation between a and b?

Consider the polynomial P(x)=ax^3-x^2-bx-1 .What is the relation between a and b if x-1 is a factor of P(x) ?

Consider the polynomial P(x)=ax^3-x^2-bx-1 .What is the relation between a and b if x+1 is a factor of P(x) ?

The sides of a triangle are 4 centimetres, 6 centimetres and 8 centimetres. What is its perimeter? Denoting the length of the sides as a , b , c and perimeter as p how do we write the relation between them?

Find the distance between P(x_1, y_1) and Q(x_2, y_2) when : (i) P Q is parallel to the y axis, (ii) P Q is parallel to the x - axis.

When the sides of asquare are increased by 8cm each,its area becomes 1225sq. cm Frame an equation using the above data by taking the side of the smaller square as x cm. Find the sides of both the squares.

p(x)=x^2-4 x+4 a) Prove that (x-2) is a factor of p(x) . b) Prove that for any number x , p(x) is always non negative.

Write P(x)=x^2-9 x+20 as a product of two first degree polynomials. Write also the solutions of the equation P(x) =0 .

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

    |