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| Math Central | Quandaries & Queries |
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Question from Amit, a teacher: A rectangular sheet of a paper with dimensions a and b is folded along its diagonal. What is the area of the overlapped region? |
Amit,
I folded the sheet of paper CDBP along the diagonal CB so that P moved to A. then drew a line segment EF to meet BC in a right angle at F. Let |CA| = a, |AB| = b and then |BC| = c where c2 = a2 + b2 by Pythagoras' Theorem.
By the symmetry F is the midpoint of BC. Let |EF| = h, the height of triangle CEB.
Triangles ABC and EBF are similar.
Can you complete the problem now?
Harley
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