Question

In what ratio Q divides CD in the figure given below? Please give Detailed Solution​

Answer 1

Answer:

Ratio => 4:5

Step-by-step explanation:

For this method we draw a line segment CD and two acute angles , angle DCX and angle CDY . after that we cut CX in 4 equal parts and DY in 5 equal parts . At last we join

C4 and D5 .

> C4+D5

>4+5

>4:5

here you go with the correct answer.

Answer 2

Given:-

The rays $\overrightarrow{CC_{4}}$ and $\overrightarrow{DD_{5}}$ are parallel to each other.

The length of one segment is equal to the other.

$\overline{CC_{4}}$ is divided into four equal segments.

$\overline{DD_{5}}$ is divided into five equal segments.

To find:-

In what ratio Q divides $\overline{CD}$ in the figure.

Methods used:-

Similarity of triangles. (AA postulate)

Solution:-

First, set the length of one segment to be $l$.

The length of the two segments are $\overline{CC_{4}}=4l$ and $\overline{DD_{5}}=5l$.

Since two rays are parallel:-

• $\angle C_{4}CQ=\angle D_{5}DQ$
• $\angle CC_{4}Q=\angle DD_{5}Q$

$\rightarrow \triangle CC_{4}Q\sim \triangle DD_{5}Q\ \mathrm{(\because AA\ postulate)}$

Hence,

$\overline{CQ}:\overline{DQ}=\overline{CC_{4}}:\overline{DD_{5}}$

$\rightarrow \overline{CQ}:\overline{DQ}=4:5$

$\rightarrow \boxed{\overline{CQ}:\overline{QD}=4:5}$

Hence, Q divides $\overline{CD}$ internally in a 4:5 ratio.