Answer:
108.7
Step-by-step explanation:
If both shapes are similar that means that they're corresponding side lengths have the same ratio. Additionally, from just looking at the images we can see that IJKL is clearly a scaled up version of EFGH, thus the side length must be multiplied by that same factor or ratio.
[tex]\frac{HG}{LK} =\frac{HE}{LI} =\frac{FG}{JK} =\frac{EF}{IJ}[/tex]
We want to find JK and we have the lengths of HG, FG and LK so, instead of setting up 4 fractions equal to each other like above we only equate 2, specifically the fractions that has JK,HG,FG and LK.
[tex]\frac{HG}{LK} =\frac{FG}{JK}[/tex]
plugging in their respective values we get,
[tex]\frac{11}{52} =\frac{23}{JK}[/tex]
now we solve!
[tex]11JK=23(52)[/tex] (cross multiply/butterfly method)
[tex]JK=\frac{23(52)}{11}=108.7[/tex]
Let me know if you have any questions!
