Hiking trail for Guadalupe mountains national park use a scale in which 2 cm represents 5 km. There are 130 km of hiking trails in the park. How many centimeters of hiking trails are on the map?

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?

How do you determine whether a relationship represented as as graph is linear or nonlinear

Given a: b and b: c, find a: b: c. write the ratio in simplest form. a: b=6: 10 and b: c=21: 33