Question

Find ED if AC=9x+1 and BD=13x-11 and ABCD is a rectangle.

Answer 1

ED = 14

Since ED splits the diagonal BD in half, we can set up an equation for later: ED = (1/2)BD.

Now, both BD and AC are diagonal lines that are congruent. This can be shown in this equation: AC = BD. Then, substitute the given information into it: 9x+1 = 13x-11 and solve!

Combine like terms and isolate the variable (see photo). And we find that x = 3.
Plug in this x value into the equation for BD = 13(3)-11 and find that BD = 28.

Back to the first equation we made, ED = (1/2)BD. So, ED = (28/2) = 14.

ED = 14.
See photo for work, I hope this helps!