Chapter 8.5, Problem 4PSA

Solution

To Calculate: Measures of KM, MO and OP

The measures of KM, MO and OP are $3.34,5$ and $6.67$ respectively.

Given information: $a\parallel b\parallel c\parallel d$ and KP = $15$

Calculation: Here, $\angle F=\angle G$ (corresponding angles)

And, $\angle G=\angle N$

So that, $\frac{2}{3}=\frac{KM}{MO}$ .......... $\left(1\right)$

  $\frac{3}{4}=\frac{MO}{OP}$ ........... $\left(2\right)$

Here, $KM=KP-MP$

➔ $KM=15-MP$ ( $\because$$KP=15$ )

Putting this value in equation $\left(1\right)$

  $\frac{2}{3}=\frac{KM}{MO}$

➔ $\frac{2}{3}=\frac{15-MP}{MO}$

➔ $2MO=45-3MP$

➔ $2\times \frac{3}{7}MP=45-3MP$

➔ $27MP=45\times 7$

➔ $MP=\frac{35}{3}$

Now, $\frac{3}{4}=\frac{MO}{MP-MO}$

➔ $3MP=7MO$

➔ $\frac{3}{7}MP=MO$

So, $\frac{3}{7}\times \frac{35}{3}=MO$

  $MO=5$

Putting this value in equation $\left(2\right)$

➔ $\frac{3}{4}=\frac{5}{OP}$

➔ $OP=6.67$

Now, putting the value of MO in equation $\left(1\right)$

➔ $\frac{2}{3}=\frac{KM}{MO}$

➔ $KM=\frac{10}{3}=3.34$