Finding the short base of a right trapezoid with a little bit of geometry

Question

We have a right trapezoid with 2 diagonals that are perpendicular with each other. <A = 90, AB = 6 sm, AD = 4 sm, DC = ?

image: https://i.imgur.com/5aJEvNm.jpg

thanks!

Answer 1

Let A = (0, 0), B = (6, 0), and D = (0, 4). This meets the right angle condition and lengths.

Then, the slope of a line from B to D will have slope -4/6 = -2/3; thus, an orthogonal diagonal will have slope 3/2 (the negative reciprocal of -2/3);

This other diagonal starts at (0, 0), so its equation is y = 3/2 b

Then, to make this figure a trapezoid, this diagonal must have the same y-coordinate as D, 4.

Then, y = 3/2 x, so 3/2 x = 4, or x = 2/3 * 4 = 8/3

Thus, C has coordinate (8/3, 4), and the length of DC, from (0, 4) to (8/3, 4), will have length 8/3.