13. A rectangle is split into triangles by drawing in its diagonals. What is the ratio of the area of triangle $P$ to the area of triangle $Q$ ?
A $1: 1$
B 1:2
C 2:1
D $2: 3$
$E$ the ratio depends on the lengths of the sides of the rectangle
Solution
A We see from the diagram on the right that the triangles $P$ and $Q$ have the same height, as is shown by the broken line. Because the diagonals of a rectangle bisect each other the triangles have bases with the same length. The area of a triangle is half the base multiplied by the height. It follows that the triangles have the same area. So the ratio of their areas is $1: 1$.