Exercise 20a
1. find the area of the rectangle whose dimensions are:
length = 24.5 m, breadth = 18 m

(ii) length = 12.5 m, breadth = 8 dm.
2.find the area of a rectangular plot, one side of which
rectangular plot, one side of which is 48 m and its diagonal is 50 m.
3.the sides ol a rect
angular park are in the ratio 4: 3. if its area is 1728 m", find the cost of
fencing it at 30 per metre.
4.area of a rectangular field is 3584 m2 and its length is 64 m. a boy runs around
field at the rate of 6 km/h. how long will he take to go 5 times around it
5. a verandah is 40 m long and 15 m broad. it is to be paved with stones, each measuring 6
dm by 5 dm. find the number of stones required.
6. find the cost of carpeting a room 13 m by 9 m with a carpet of width 75 cm at the rate of
3105 per metre
7. the cost of carpeting a room 15 m long with a carpet of width 75 cm at 80 per metre 18
19200. find the width of the room.
8.the length and breadth of a rectangular piece of land are in the ratio of 5: 3. if the total cost
of fencing it at 24 per metre is 9600, find its length and breadth.

answer: the answer is b. i think hope i got it correct

step-by-step explanation:

i think it's eleven too, don't woosh me here, but according to the "experts" it's 2.

the proof starts from the peano postulates, which define the natural

numbers n. n is the smallest set satisfying these postulates:

  p1.   1 is in n.

  p2.   if x is in n, then its "successor" x' is in n.

  p3.   there is no x such that x' = 1.

  p4.   if x isn't 1, then there is a y in n such that y' = x.

  p5.   if s is a subset of n, 1 is in s, and the implication

      (x in s => x' in s) holds, then s = n.

then you have to define addition recursively:

  def: let a and b be in n. if b = 1, then define a + b = a'

      (using p1 and p2). if b isn't 1, then let c' = b, with c in n

      (using p4), and define a + b = (a + c)'.

then you have to define 2:

  def:   2 = 1'

2 is in n by p1, p2, and the definition of 2.

theorem:   1 + 1 = 2

proof: use the first part of the definition of + with a = b = 1.

      then 1 + 1 = 1' = 2   q.e.d.

note: there is an alternate formulation of the peano postulates which

replaces 1 with 0 in p1, p3, p4, and p5. then you have to change the

definition of addition to this:

  def: let a and b be in n. if b = 0, then define a + b = a.

      if b isn't 0, then let c' = b, with c in n, and define

      a + b = (a + c)'.

you also have to define 1 = 0', and 2 = 1'. then the proof of the

theorem above is a little different:

proof: use the second part of the definition of + first:

      1 + 1 = (1 + 0)'

      now use the first part of the definition of + on the sum in

      parentheses:   1 + 1 = (1)' = 1' = 2   q.e.d.