Answer: The answer is (D) 27.
Step-by-step explanation: Given that in the figure, triangles GHI and MHL are similar to each other. We are to find the value of 'x'.
Also, given that
GH = 18, HI = 16, HL = 24 and HM =x.
Since the given triangles are similar, so their corresponding sides are proportional.
That is,
[tex]\dfrac{GH}{HM}=\dfrac{HI}{HL}=\dfrac{GI}{ML}.[/tex]
So, we have
[tex]\dfrac{18}{x}=\dfrac{16}{24}\\\\\Rightarrow x=\dfrac{18\times 24}{16}\\\\\Rightarrow x=27.[/tex].
Thus, the value of 'x' is 27.
