Question

Angle CAB=90 AB=AC=DE BD=9 CE=8 Find DE

Answer 1

Answer:

  29

Step-by-step explanation:

Let x represent the length of DE. Then ...

  AB = x

  AD = AB -BD = x - 9

__

  AC = x

  AE = AC -CE = x - 8

And the Pythagorean theorem applied to triangle ADE tells us ...

  x^2 = (x -9)^2 +(x -8)^2

  0 = x^2 -34x +145 = (x -5)(x -29)

Solutions are the values of x that make a factor zero: 5 or 29.

The length of DE must be greater than 9, so the appropriate solution from the above equation is x = 29.

The length of DE is 29.