Find the longest rectangular plank of wood which can fit diagonally across a 6m by 8m room as shown below.
The two big triangles and two small triangles are similar; call their ratio r. Label the sides of the small triangle a and b thus –
The diagonal of the room forms a 6m:8m:10m triangle, and similarly the small triangle is 0.3m:0.4m:0.6m. Now we have this triangle –
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Hmmm...
