Pythagorean theorem

$a^2=b^2+c^2$

$a^2=17^2+8.5^2$

You'll have to use whatever method you prefer for multiplication without calculator. I like to use this method.

$a^2=289+72.25$

$a^2=361.25$

$a=\sqrt{361.25}$

This is an answer for root form. To convert it to decimal, we can do some trial and error.

$20^2=400$

$19^2=361$

That's probably the closest we're going to get, so we give the decimal answer as:

$a\approx19$

I am assuming that A,c and E are collinear.

 

Use pythagorean theorum :)

 

$AE^2=8.5^2+17^2\\$

 

AE^2=8.5^2+17^2\\

 

Here is a nefty trick for finding the square of numbers ending in 5

85^2      

 = 8^2+8    with 25 tacked on the end.

= 64+8    with 25 tacked on the end.

= 72    with 25 tacked on the end.

=7225

 

so  8.5^2=72.25

17^2=289   (I just know that)      

But I could do it as (10+7)^2 = 100+140+49=289

so

 

$AE^2=8.5^2+17^2\\ AE^2=72.25+289\\ AE^2=361.25\\ AE^2=\frac{36125}{100}\\ AE^2=\frac{25*1445}{100}\\ AE^2=\frac{25*5*289}{100}\\ AE=\frac{5*\sqrt5*17}{10}\\ AE=\frac{85\sqrt5}{10}\\ AE=8.5\sqrt5\\$

That is in  8.5sqrt5    cm of course.

Will has given you a good decimal approximation.  Thanks Will