a rectangular box of salt measures 4 inches by 5 inches by 8 inches. When resting on its smallest face, the level of the salt is 2 inches from the top. How many inches from the bottom will the level of the salt reach if the box is turned and placed on its largest place

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?

Terri makes a quilt using three sizes of fabric squares the side lenght of each fabric square is the square root of the area

Two cyclists 84 miles apart start riding toward each other at the same. one cycles 2 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?