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2 years ago

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

Mathematics

1 answer:

zalisa [80]2 years ago

3 0

Answer:

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.

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