Q. 14.0( 18 Votes )

In rectangles wit

Answer :

Given one side is smaller than the other by 1 cm.

The two adjacent sides of the triangle are x, x + 1.


(i) perimeter p(x) = 2 × [(x) + (x + 1)]


p(x) = 4x + 2 – (1)


(ii) Area a(x) = (x) × (x + 1)


a(x) = x2 + x – (2)


(iii) by (1)


p(1) = 4 × 1 + 2 = 6


p(2) = 4 × 2 + 2 = 10


p(3) = 4 × 3 + 2 = 14


p(4) = 4 × 4 + 2 = 18


p(5) = 4 × 5 + 2 = 22


Here the difference between a number and its successor is always 4.


We can see that they are in Arithmetic Progression (AP) with a common difference of 4.


(iv) by (2)


a(1) = 12 + 1 = 2


a(2) = 22 + 2 = 6


a(3) = 32 + 3 = 12


a(4) = 42 + 4 = 20


a(5) = 52 + 5 = 30


Here the difference between a number and its previous number is increasing by 2.


a(2) – a(1) = 4


a(3) – a(2) = 6


a(4) – a(3) = 8


a(5) – a(4) = 10


Their common difference is in AP.


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