Where does the halving line cross the bottom edge?
A hard-level "Length" problem.A rectangle is halved by any line through its centre. So for any shape built from rectangles, one line through all the centres halves the whole thing.
GivenTwo rectangles joined: the lower is 10 × 4 cm, the upper 4 × 8 cm
Hints
- There are in fact infinitely many lines that halve the area. We want a way to pin down just one of them, for certain.
- The key is a property of rectangles: any line through the centre (where the diagonals cross) splits a rectangle into two equal halves, whatever its direction. All three thin lines halve it.
- The shape is two rectangles; here are their centres. A line through both centres at once halves both rectangles at the same time.
- Half plus half means the whole shape is halved too. That is our line — all that is left is where it meets the bottom edge.
- From centre to centre is 3 across and 6 up. On a straight line that ratio never changes.
- From the lower centre down to the bottom edge is just 2. Going down 6 moves you 3 to the left, so going down 2 moves you 3 × 2 ÷ 6 = 1 left of the centre at 5 cm.
Answer 4cm
More "Length" problems
- a + b + c = ?
- What is the side of the square?
- How long is MN?
- How long is the rope?
- How long is the pole's shadow?
- How deep was the water?