Could someone please look at this? I think the answer is 26 for the length of KL because KL=2(13). Is this right?
Why would you assume KL = 2(13)?
See the slightly modified diagram below.
MJKN is a square, so the diagonal bisects the angles at the corners. so we have 45 degree angles in the positions shown
Remember, $\displaystyle MK = \sqrt {50}$ and $\displaystyle KI = 13$
Now, $\displaystyle \sin 45^{ \circ} = \frac {JK}{MK} = \frac {JK}{ \sqrt {50}}$
$\displaystyle \Rightarrow JK = \sqrt {50} \sin 45^{ \circ} = 5$
Now note that JK = MN = IL
By Pythagoras' Theorem:
$\displaystyle IJ = LK = \sqrt { (IK)^2 + (IL)^2} = \sqrt {13^2 + 5^2} = 12$
Hello, sanee66!
Sorry, your answer makes no sense . . .
In square $\displaystyle JMNK$, diagonal $\displaystyle MK$ measures $\displaystyle \sqrt{50}$
and in rectangle $\displaystyle IJKL$, diagonal $\displaystyle KI$ measures $\displaystyle 13$.
What is the length of IJ (or KL)?Code:I J M * - - - - - - - - - - - * - - - - - * | * | __ * | | * 13 | √50 * | x | * | * | x | * | * | | * | * | * - - - - - - - - - - - * - - - - - * L y K x N
The sides of the square have length $\displaystyle x$.
From Pythagorus, we have: .$\displaystyle x^2 + x^2 \:=\:(\sqrt{50})^2$
Hence: .$\displaystyle 2x^2 = 50\quad\Rightarrow\quad x^2 = 25\quad\Rightarrow\quad x = 5$
In right triangle $\displaystyle ILK$, we have: .$\displaystyle IL = 5,\:IK = 13$
From Pythagorus, we have: .$\displaystyle y^2 + 5^2\:=\:13^2\quad\Rightarrow\quad y^2 = 144\quad\Rightarrow\quad y = 12$
Therefore: .$\displaystyle KL \,=\,IJ \,=\,12$