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Mathematics, 26.02.2021 14:00 tts313
A rectangular gate has a diagonal bar running across it. The gate is 80 cm high and 2 m wide. Work out the length of the bar. Give your answer in surd form.
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Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?
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A rectangular gate has a diagonal bar running across it. The gate is 80 cm high and 2 m wide. Work...
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