Chapter 12.5, Problem 4CK

To determine

Tofind:The reason for $\frac{y}{4}=\frac{3-x}{x}$ .

Answer to Problem 4CK

The ratio of corresponding sides of triangle is equal. So, the proportion $\frac{y}{4}=\frac{3-x}{x}$ holds.

Explanation of Solution

Given information:The figure is shown below:

  

Calculation:

As it is already prove that both triangles are similar. So, $\Delta VOB\sim \Delta EDB$ .By the similarity of two triangles the corresponding sides of similar triangles are equal in ratio:

  $\frac{ED}{VO}=\frac{DB}{OB}$

Substitute $y$ for ED , $4$ for VO , $3-x$ for DB and $3$ for OB in the above proportion.

  $\begin{array}{c}\frac{y}{4}=\frac{3-x}{3}\\ y=\frac{4\left(3-x\right)}{3}\end{array}$

Therefore, the proportion $\frac{y}{4}=\frac{3-x}{x}$ holds.