Question

in the diagram below, nk = 10.7, lm = 27.3, and ln = 21.3. find the length of mj. round your answer to the nearest tenth if necessary. first, copy the figure and write in the correct side - lengths. mn || jk side splitter: if a line intersects two sides of a triangle and is parallel to the third, it divides the 2 sides proportionally.

Explanation:

Step1: Apply side - splitter theorem

Since $MN\parallel JK$, we have the proportion $\frac{LM}{MJ}=\frac{LN}{NK}$. Let $MJ = x$. Then $\frac{37.3}{x}=\frac{21.3}{10.7}$.

Step2: Cross - multiply

Cross - multiplying gives us $21.3x=37.3\times10.7$.

Step3: Calculate the right - hand side

$37.3\times10.7 = 399.11$. So, $21.3x = 399.11$.

Step4: Solve for $x$

$x=\frac{399.11}{21.3}\approx18.7$.

Answer:

$18.7$