Question

find x in these 45°-45°-90° triangles. x=?
https://media.glynlyon.com/g_geo_2012/11/groupi40.gif

Answer 1

hmmm https://
well, a secure website, lemme try that one :/

Answer 2

45-45-90 rule
http://nanharbison.com/sats/math_images/45-45-90.gif

Answer 3

that doesn't help :(

Answer 4

well, how so? :/

Answer 5

what the "rule" is saying is that
if you have a 45-45-90 triangle
the RATIO or RELATIONSHIP of the sides is as shown there

Answer 6

look at your longest side, the hypotenuse, is "8"
look at the relationship
on the 45-45-90 rule, 8 = \(x\sqrt{2}\)

Answer 7

and "x", will be the other "2 twin sides"

so just solve
\( \large 8 = x\sqrt{2}\)
for "x" :)

Answer 8

so x = 64?

Answer 9

well, is \( \large 8 = x\sqrt{2}\) not \(\large 8 = \sqrt{x}\)

Answer 10

how do you solve 8=x^2?

Answer 11

divide both sides by \(\sqrt{2}\) to isolate or "solve" for "x"

$$
8 = x\sqrt{2} \implies \cfrac{8}{\sqrt{2}} =x
$$

Answer 12

sorry but I still don't know what you do when you get 8/square root of 2

Answer 13

well, that's "x", you can simplify it further I gather by getting rid of the root in the denominator by
$$
8 = x\sqrt{2} \implies \cfrac{8}{\sqrt{2}} =x\\
\cfrac{8}{\sqrt{2}} \times \cfrac{\sqrt{2}}{\sqrt{2}}
\implies \cfrac{\cancel{8}\sqrt{2}}{\cancel{2}} \implies 4\sqrt{2}
$$

Answer 14

oh yeah thanks much you've been a big help!

Answer 15

yw