The formula for the area of a triangle is a = zon, where b is the length of the base and h is the height. Find the height of a triangle that has an area of 30 square units and a base measuring 12 units.

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?

Carly stated, “all pairs of rectangles are dilations.” which pair of rectangles would prove that carly’s statement is incorrect?

Round each decimal to the nearest thousandth. a. 5.39562 b. 0.12345 c. 5634 d. 18.93763