Question

If HL=12, LI-8, and HK =25, find KJ to the nearest hundredth.

Answer 1

KJ = 16.67 units

Step-by-step explanation

The small triangle, HLK, is similar to the big triangle, HIJ

So, we can write

`(HL)/(HI)=(LK)/(IJ)=(HK)/(HJ)`

HL = 12 units

LI = 8 units

So, HI = Hl + LI = 12 + 8 = 20 units

HK = 25 units

HJ = HK + KJ

KJ = ?

`\begin{gathered} (HL)/(HI)=(HK)/(HJ) \\ (12)/(20)=(25)/(HJ) \\ HJ*12=25*20 \\ 12HJ=500 \\ \text{Divide both sides by 12} \\ (12HJ)/(12)=(500)/(12) \\ HJ=41.667\text{ units} \end{gathered}`

HJ = HK + KJ

41.667 = 25 + KJ

KJ = 41.667 - 25 = 16.67 units

Hope this Helps!!!