In a quadrilateral ABCD, it is given
that AB is parallel to CD and the
diagonals AC and BD are perpendicular
to each other.
Show that
(a) AD.BC ≥ AB.CD;
(b) AD + BC ≥ AB + CD.
Let ABC be a triangle and h_a the
altitude through A. Prove that
(b + c)^2 ≥ a^2 + 4h_a ^2 .
(As usual a, b, c denote the sides BC,
CA, AB respectively.)
Q. In 2014, country X had 783 miles of paved roads. Starting in
2015, the country has been building 8 miles of new paved
roads each year. At this rate, how many miles of paved roads
will country X have in 2030?