Question

how many different rectangels with an area of one hundred twenty (120) square units can be formed using unit squares? Using 4 polyas strategy
Understand the problem
Devise a plan
Carry out the plan
Revise the solution

Answer 1

Above is you r answer

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Answer 2

Given :- How many different rectangels with an area of one hundred twenty (120) square units can be formed using unit squares of natural numbers ?

Solution :-

we have ,

• Length * Breadth = 120 unit² .

since both length and breadth as natural numbers then ,

• If Length = 1 , => Breadth = (Area/Length) = 120/1 = 120
• If Length = 2 , => Breadth = (Area/Length) = 120/2 = 60
• If Length = 3 , => Breadth = (Area/Length) = 120/3 = 40
• If Length = 4 , => Breadth = 30
• If Length = 5 , => Breadth = 24
• If Length = 6 , => Breadth = 20
• If Length = 8 , => Breadth = 15
• If Length = 10 , => Breadth = 12

Similarly,

• If Breadth = 1 unit, => Length = 120 unit .
• If Breadth = 2 unit, => Length = 60 unit .
• If Breadth = 3 unit, => Length = 40 unit .
• If Breadth = 4 unit, => Length = 30 unit .
• If Breadth = 5 unit, => Length = 24 unit .
• If Breadth = 6 unit, => Length = 20 unit .
• If Breadth = 8 unit, => Length = 15 unit .
• If Breadth = 10 unit, => Length = 12 unit .

Therefore,

→ Total number of different rectangle Possible = 8 + 8 = 16 Rectangles (Ans.)

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