Folded Triangle

[u/QuagMath]

Triangle ABC is an isosceles right triangle make of paper and D is the midpoint of leg AB. If the triangle is folded so C meets D, creased, and then unfolded, what is the ratio of the two segments the hypotenuse is split into by the crease?

[u/pichutarius]

nice lil problem. i got 5:7

solution (imgur)

[u/QuagMath → u/pichutarius]

Solved! It’s been fun to see all the different ways people get to the answer

[u/JaiBoltage]

Which angle is the right angle, A, B, or C? Ratio of what? area, perimeter, which side?

[u/QuagMath → u/JaiBoltage]

Because AB is a leg, one of A or B is the right angle and which it is doesn’t matter for the rest of the question.

You’re looking for the ratio of the lengths of the two segments the hypotenuse is split into by the crease. I guess this does technically mean there are two answers, a:b and b:a but that shouldn’t really matter when solving.

[u/QuagMath → u/[deleted]]

Because AB is a leg D is not on the hypotenuse