how many rectangles of different sizes can be formed from 36 identical squares
Answers
Answer:
For a total of 5 rectangles that have 36 squares each.
Step-by-step explanation:
Given :-
36 identical squares
To find :-
How many rectangles of different sizes can be formed from 36 identical squares ?
Solution :-
Given that
Total number of identical squares = 36
Let the measurement of the side of each square be 1 unit
So Area of a square = Side × Side sq.units
=> Area of each square = 1×1 = 1 sq.unit
Area of total 36 identical squares
=> 36×1 sq.units
=> 36 sq.units
Now
So Area of the rectangle = lb sq.units
So if the rectangles are formed from 36 identical squares then both areas are same.
=> Total area of required rectangles = 36 sq.units
36 sq.units can be written as
=> 36 = l×b
36 = 1×36
36 = 2×18
36 = 3×12
36 = 4×9
36 = 6×6
(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares
Total rectangles = 5
Answer:-
Total number of different rectangles formed from 36 identical squares is 5
Used formulae:-
- Area of a square = Side × Side sq.units
- Area of the rectangle = lb sq.units
- A square is also a rectangle