Question

In △PQR, what is the length of line segment QR?
http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0404_02/image0064e2eda71.gif

28

28radical 2

56radical 3

56radical 2

*I think the answer is A?*

Answer 1

this is a "special right triangle"
45-45-90

The idea is to remember that the hypotenuse (longest side, opposite the 90 deg angle) is sqrt(2) times bigger than either leg (which are equal)
h = a*sqrt(2)

or (divide by sqrt(2) )
a= h/sqrt(2)

Answer 2

or (because people do not sqrt(2) in the denominator)
a= sqrt(2)*h/(sqrt(2)*sqrt(2)) (multiply top and bottom by sqrt(2))
you do this to get rid of the sqrt(2) in the bottom
a= sqrt(2)*h/2

Answer 3

Whoa. That was a lot.

Answer 4

too much to get the answer?

Answer 5

I'm not sure. I'm looking at it like @ . @

Answer 6

the side is h/sqrt(2)= 56/sqrt(2)
but none of your answers are in that form.
so we have to "rationalize" to get an answer that matches.

Answer 7

@Parthkohli this one :D

If you are given a leg of a 45-45-90 triangle, you just put 2√ in front of it to get the hypotenuse ^_^ • If the leg is 8, then the hypotenuse is 82√ • If the leg is 1281283283283249483483, then the hypotenuse is 12812832832832494834832√

Answer 8

The short-cut that I gave you doesn't work here too much, FYI. I just told you in simple words to remove/put sqrt2.

What that short-cut actually says is that you have to multiply sqrt2 to get the hypotenuse and divide sqrt2 from the hypotenuse to get the leg.

Answer 9

can we just use trigo. here?

\[\cos \theta =\frac{adjacent}{hyp}\]

Answer 10

So, you divide \(\sqrt2\) from the hypotenuse to get the leg.

Answer 11

adjacent=(cos 45)*56

Answer 12

Or, the Pythagorean.

\( \color{Black}{\Rightarrow a^2 + a^2 = 56^2 }\)

\( \color{Black}{\Rightarrow 2a^2 = 3136}\)

Answer 13

If you ever get confused with that short-cut, just come back to Pythagorean ;)

Answer 14

Ah! okay um wait...that just goes back to 28?

Answer 15

\( \color{Black}{\Rightarrow a^2 = 1568}\)

You find \(\sqrt{1568}\).

Answer 16

(In radical form).

Answer 17

Okay √1568 = 39.5 and 28√2 = 39.5 as well :D

Answer 18

Yep :)

Answer 19

Yay :D Thanks