PLS ANYBODY SOLVE THIS AND TELL WHICH CLASS ARE YOU AT LAST OK NOW HELP ME PLS
Answers
Required Knowledge
- Rule of addition
→ If each event is happening separately, we add the number of events.
- Rule of product
→ If each event is happening consecutively, we multiply the number of events.
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Solution
Consider separating the squares into figure A and figure B.
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Figure A
Consider choosing a side around the grid of lengths of 1 or 2, horizontally or vertically.
Side Lengths
Length of 1
⇒ 2 different sides
Length of 2
⇒ 1 side
Squares with Side Lengths
There forms a unique square, as we choose from vertical or horizontal lines. This means we can form a square by the rule of product.
Length of 1
⇒ 2 × 2 = 4 squares
Length of 2
⇒ 1 × 1 = 1 square
Squares in Total (Fig. A)
By the rule of addition, we conclude that there are 2 × (4 + 1) = 10 squares in figure A.
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Figure B
Consider choosing a side around the grid of lengths of 1, 2, 3, 4, vertically or horizontally.
Side Lengths
Length of 1
⇒ 4 different sides
Length of 2
⇒ 3 different sides
Length of 3
⇒ 2 different sides
Length of 4
⇒ 1 side
Squares with Side Length
There forms a unique square, as we choose from vertical or horizontal lines. This means we can form a square by the rule of product.
Length of 1
⇒ 4 × 4 = 16 different squares
Length of 2
⇒ 3 × 3 = 9 different squares
Length of 3
⇒ 2 × 2 = 4 different squares
Length of 4
⇒ 1 × 1 = 1 square
Squares in Total (Fig. B)
By the rule of addition, we conclude that there are 16 + 9 + 4 + 1 = 30 squares in figure B.
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So, we can say that there are 10 + 30 = 40 squares. This is the required answer.
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Short Note
Since I don't know your class, I left a detailed solution. If you have a question don't mind asking it!
