Problem 11 · 2020 Math Kangaroo
Medium
Geometry & Measurement
spatial-reasoning
Denis ties his dog with an 11-metre rope, one metre away from a corner of a fence about 7 metres by 5 metres, as shown. Denis places 5 bones near the fence, as in the picture. How many bones can the dog reach?
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Answer: E — 5
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Hint 1 of 3
The dog is tied just outside the fence, so the rope has to hug the fence and bend around each corner to reach a bone.
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Hint 2 of 3
Walk the rope along the fence step by step, counting the metres (the tick marks) and bending it at every corner.
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Hint 3 of 3
Check how far 11 metres of rope can reach once it turns the corners.
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Approach: follow the rope along the fence, counting metres and bending at corners
- The dog is tied 1 metre from the top-right corner, so the rope wraps along the top edge, down a side, and around the bottom, bending at each corner.
- Counting the tick marks (each 1 metre), the farthest bone along this path is still within the 11 metres of rope once it bends around the corners.
- So the rope is long enough to reach every bone, and the dog can grab all 5 of them, choice E.
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