Chapter 7.4, Problem 38PPS

To determine

To find: The length of ML , QR , QK , and JH of the given figure.

Answer to Problem 38PPS

The length of ML , QR , QK , and JH of the given figure are $2\text{unit}$ , $3\text{unit}$ , $6\text{unit}$ , and $4\text{unit}$ .

Explanation of Solution

Given information:

The given figure is,

  

The length of ML is calculated as,

  $\begin{array}{l}\frac{ML+LK}{ML}=\frac{MP+PQ}{MP}\\ 1+\frac{LK}{ML}=1+\frac{PQ}{MP}\\ \frac{4}{ML}=\frac{6}{3}\\ ML=2\text{unit}\end{array}$

The length of QR is calculated as,

  $\begin{array}{l}\frac{ML+LK+KJ}{ML+LK}=\frac{MP+PQ+QR}{MP+PQ}\\ 1+\frac{KJ}{ML+LK}=1+\frac{QR}{MP+PQ}\\ \frac{2}{2+4}=\frac{QR}{3+6}\\ QR=3\text{unit}\end{array}$

The length of QK is calculated as,

  $\begin{array}{l}\frac{QK}{MP+PQ}=\frac{LP}{MP}\\ \frac{QK}{3+6}=\frac{2}{3}\\ QK=6\text{unit}\end{array}$

The length of JH is calculated as,

  $\begin{array}{l}\frac{ML+LK+KJ+JH}{ML+LK+KJ}=\frac{MP+PQ+QR+RS}{MP+PQ+QR}\\ 1+\frac{JH}{ML+LK+KJ}=1+\frac{RS}{MP+PQ+QR}\\ \frac{JH}{2+4+2}=\frac{6}{3+6+3}\\ JH=4\text{unit}\end{array}$

Thus, The length of ML , QR , QK , and JH of the given figure are $2\text{unit}$ , $3\text{unit}$ , $6\text{unit}$ , and $4\text{unit}$