Question

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

Answer 1

Answer

KJ = 16.67 units

Explanation

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

So, we can write

$\frac{HL}{HI}=\frac{LK}{IJ}=\frac{HK}{HJ}$

HL = 12 units

LI = 8 units

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

HK = 25 units

HJ = HK + KJ

KJ = ?

$\begin{gathered} \frac{HL}{HI}=\frac{HK}{HJ} \\ \frac{12}{20}=\frac{25}{HJ} \\ HJ\times12=25\times20 \\ 12HJ=500 \\ \text{Divide both sides by 12} \\ \frac{12HJ}{12}=\frac{500}{12} \\ HJ=41.667\text{ units} \end{gathered}$

HJ = HK + KJ

41.667 = 25 + KJ

KJ = 41.667 - 25 = 16.67 units

Hope this Helps!!!