Question

How many rectangles (including squares) are there in a 4x4 square

Answer 1

Answer:

Hello,

100

Step-by-step explanation:

a square 4*4 : wide=4 , lenght=4

number of rectangles= wide*(wide+1)*lenght*(lenght+1) /4 = 4*5*4*5/4=100

Proof:

1 per 1 : 16 (rectangles )

1 per 2: 3*4=12

1 per 3: 2*4=8

1 per 4: 1*4=4 so 4*(4+3+2+1)=4*10=40

2 per 1: 4*3

2 per 2: 3*3

2 per 3: 2*3

2 per 4: 1*3 so 3*(4+3+2+1)=30

3 per 1: 4*2

3 per 2: 3*2

3 per 3: 2*2

3 per 4: 1*2 so 2*(4+3+2+1)=20

4 per 1: 4

4 per 2: 3

4 per 3: 2

4 per 4: 1 so 1*(4+3+2+1)=10

Total=40+30+20+10=(4+3+2+1)*(4+3+2+1)=100

Answer 2

Answer:

70 squares

Step-by-step explanation:

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