Chapter 12.5, Problem 5CK

To determine

To prove:The statement $y=\frac{4}{3}\left(3-x\right)$ by multiplication property of equality.

Explanation of Solution

Given information:The given expression is $y=\frac{4}{3}\left(3-x\right)$ and the figure is:

  

Proof:

Multiplication property of equality states that, equality is preserved when the same number is multiplied to the both sides of the given equation.

In the given figure, $OB=3$ , $VB=5$ , $ED=y$ , $OD=x$ and $DB=3-x$ .

According to the similarity property of triangles:

  $\frac{y}{4}=\frac{3-x}{3}$

Multiply both the sides by $4$ .

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

Hence, above statement is proved by the multiplication property of equality.