Question

Tyler is writing a coordinate proof to show that a diagonal of a rectangle divides the rectangle into two triangles that have equal areas. He starts by assigning coordinates to a rectangle. Then he uses these coordinates to Arian expression for the are of each triangle formed by the diagonal. What is the area of one of the triangles formed by the diagonal of the rectangle

Answer 1

The answer is ab/2 good luck

Answer 2

Explanation:

We are given that Tyler is proving that diagonal of a rectangle divides the rectangle into two triangles that have equal areas.

For that he assigned coordinates to a rectangle.

Let us assume ABCD be the rectangle with vertex A at origin that is (0,0).

And B at (l,0), C at (l,w) and D at (0,w).

Please refer the diagram attached.

Let us draw a diagonal from A to C.

So, area of the triangle formed by diagonal of rectangle = area of ΔABC

=
`(1)/(2)X(base)X(height)`

`=(1)/(2)X(AB)X(BC)`

`=(1)/(2)lw`

which is nothing but half of lw(area of rectangle).

Hence the area of one of the triangles formed by diagonal is half of the area of rectangle.