Algebra II Question

If j, k, and l are positive with jk = 24, jl = 48, and kl = 18, find j + k + l.

jk  = 24 ⇒  24/j  = k

jl = 48  ⇒  48/j  = l

kl = 18   

So

kl  = 18

(24/j) (48/j)  = 18

1152 / j^2  = 18

j^2  = 1152/18

j^2  = 64   take the positive root

j =  8

So.....24 / j = k   ⇒    24 / 8  = k ......  3  = k

And  48 / j  = l ⇒   48 / 8  = l    ......  6  = l

So

j + k + l    = 8 + 3  +  6  =   17

If j, k, and l are positive with jk = 24, jl = 48, and kl = 18,

find j + k + l.

1.

\(\begin{array}{|rcll|} \hline jk\cdot jl \cdot kl = (jkl)^2 &=& 24\cdot 48\cdot 18 \\ &=& 20736 \\ jkl &=& \sqrt{20736} \\ \mathbf{jkl} &\mathbf{=}& \mathbf{ 144} \\ \hline \end{array}\)

2.

\(\begin{array}{|rcll|} \hline j+k+l &=& \dfrac{jk\cdot jl}{jkl} + \dfrac{jk\cdot kl}{jkl} + \dfrac{jl\cdot kl}{jkl} \\ &=& \dfrac{jk\cdot jl+jk\cdot kl+jl\cdot kl}{jkl} \\ &=& \dfrac{24\cdot 48+24\cdot 18+48\cdot 18}{144} \\ \mathbf{j+k+l} &\mathbf{=}& \mathbf{ 17} \\ \hline \end{array}\)