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lozanna [386]
4 years ago
5

Find the missing lengths: HI=7 and LH=9, find LK.

Mathematics
1 answer:
Katarina [22]4 years ago
8 0

Answer:

LK=12    

Step-by-step explanation:

From the given figure, HI=7 and LH=9, and we know that

(KH)^{2}=(IH)(HL)

(KH)^{2}=7{\times}9

(KH)^{2}=63                             (1)

Now, from ΔKHL, we have

(OH)^{2}=(OK)(OL)

and from ΔOKH,

(KH)^{2}=(OH)^{2}+(OK)^2

(OK)^2=(KH)^2-(OH)^2

(OK)^2=63-(OK)(OL)

(OK)^2+(OK)(OL)=63

OK(OK+OL)=63

OK(KL)=63                                 (2)

Also, ΔIKL is similar to ΔOHL, therefore

\frac{OL}{KL}=\frac{9}{16}

\frac{KL-OK}{KL}=\frac{9}{16}

\frac{KL-OK}{KL}=\frac{9}{16}

1-\frac{OK}{KL}=\frac{9}{16}

\frac{7}{16}=\frac{OK}{KL}

Using equation (2), we get

\frac{7}{16}=\frac{63}{(KL)^2}

(KL)^2=\frac{1008}{7}

(KL)^2=144

KL=12

Thus, the value of LK is 12.

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