Question

In the diagram, JK:KL is 3:2 and JL = 35. Find JK and KL

Answer 1

In the diagram, JK:KL is 3:2 and JL = 35. Find JK and KL

Solution:

Let $KL = x$. Then

$$\frac {J K}{x} = \frac {3}{2}$$

and

$$J K = \frac {3}{2} x.$$

So we have

$$J K + K L = J L,$$ $$\frac {3}{2} x + x = 3 5,$$ $$\left(\frac {3}{2} + 1\right) x = 3 5,$$ $$\frac {5}{2} x = 3 5,$$ $$x = 3 5 \cdot \frac {2}{5},$$ $$x = 1 4.$$

Finally

$$K L = 1 4, J K = \frac {3}{2} x = \frac {3}{2} \cdot 1 4 = 2 1.$$

Answer:

$$K L = 1 4, J K = 2 1.$$