Q1 of 16 Page 150

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

An 1 metre wide path goes around a square ground. The relation between the length of a side of the ground and the area of the path.


Let the side of the ground be a.


The width of the path is 1 m.


⇒ Length of one side of the path is a + 2 m.


⇒ Area of the path = (a + 2)2 – (a)2


Now, Area of the path is a is defined p(a)


⇒ p(a) = (a + 2)2 – (a)2


⇒ p(a) = 4 + 4 × a


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2

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:


i) Taking side of the square as x centimetres, write the dimensions of the box in terms of x.


ii) Taking the volume of the box as v(x) cubic centimetres, write the relation between v(x) and x as an equation.


iii) Calculate

3

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 numbers as a(x), for two different numbers as x, what must be the relation between the numbers?

 1

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

A liquid contains 7 litres of water and 18 litres of acid. More acid is added to it. The relation between the amount of acid added and the change in the percentage of acid in the liquid.

 1

Write each of the relations below in algebra and see if it gives a polynomial. Give reasons for your conclusion also.

Two poles of heights 3 metres and 4 metres are erected upright on the ground, 5 metres apart. A rope is to be stretched from the top of one pole to some point on the ground and from there to the top of the other pole:



The relation between the distance of the point on the ground from the foot of a pole and the total length of the rope.