Chapter 16, Problem 2RP

To determine

To find: the ratio of $\frac{DJ}{DG}$ from a given triangle $DEFGH$ .

Answer to Problem 2RP

  $\frac{DJ}{DG}=\frac{4}{5}$ .

Explanation of Solution

Given:

  

  $EG:GF=4:6\text{ and }DH:HF=2:5.$ .

Concept used:

If two points balanced the product of the mass and distance from the line of the balance of on point will be equal to the product if the mass and distance from the same line balance of the other point.

  $\begin{array}{l}\frac{w_1}{w_2}=\frac{l_2}{l_1}.\\ w_1\times l_1=w_2\times l_2.\\ w_b=w_1+w_2.\end{array}$

Where $w$ is weight at which the weight is divided or incase of triangle the line which bisect the two weight.

Calculation:

According to the given side of the triangle are:

  $EG:GF=4:6\text{ and }DH:HF=2:5.$

  $DH\times w_f=HF\times w_d.$

Which implies weight on $D$ will be $5$ . Weight on $F$ is $2$ from the $DH$ and weight on $F$ from $EG$ is $4$ .

So, the $w_f=4\text{ or }2$ .

Therefore, the weight is taken as there multiple.

  $w_f=8$ .

Which implies

  $\begin{array}{l}EG=8.\\ GF=12.\end{array}$ .

There mid value point $G$ will be the sum of two vertices which is

  $\begin{array}{l}12+8=20.\\ w_G=DJ=20.\\ w_D=GJ=5.\end{array}$

According to the diagram:

  $\begin{array}{l}DJ+JG=DG.\\ 20+5=25.\\ DG=25.\\ \frac{DJ}{DG}=\frac{20}{25}=\frac{4}{5}.\end{array}$

Hence, the ratio is $\frac{DJ}{DG}=\frac{4}{5}$ .