Problem 16 · 2025 Math Kangaroo
Hard
Geometry & Measurement
areasymmetry
The diagram shown on the right consists of squares of equal size. Point B is in the middle of A and C, and point D is in the middle of C and E. Maria wants to divide the figure into two parts with equal areas using a straight line. Which of the points A, B, C, D or E must she connect to S to obtain this result?
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Answer: E — E
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Hint 1 of 2
First count the squares: the cut from S has to leave exactly half of them on each side.
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Hint 2 of 2
As you slide the far end of the cut from A up to E, more area moves to one side — stop at the point that makes the two halves equal.
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Approach: make each side hold half the squares
- Count the unit squares in the whole figure and take half: the straight cut from S must leave that same area on each side.
- Connecting S to a low point like A leaves too little on one side, and as the endpoint climbs from A toward E more area swings across the line.
- The endpoint that finally balances the two sides into equal areas is E, so Maria connects S to E, giving the answer (E).
Mark:
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