Chapter 7, Problem 12CR

To determine

To find: the values of x and y

Answer to Problem 12CR

The values of x and y are $9,\frac{27}{2}$

Explanation of Solution

Given Information: A figure showing two similar quadrilaterals

Formula used:

When two quadrilaterals are similar the ratio of lengths of their corresponding sides is equal and is referred to as scale factor.

Calculation: Consider the two quadrilaterals given below

  

The scale factor of the given parallelograms as per the above definition can be expressed as,

  $\frac{8}{12}=\frac{6}{x}=\frac{9}{y}$

Considering the first two pairs of ratios,

  $\frac{8}{12}=\frac{6}{x}$

On cross-multiplication, the value of x can be obtained as,

  $\begin{array}{c}8x=12\times 6\\ x=\frac{12\times 6}{8}\\ =9\end{array}$

Now, considering the first and last ratio,

  $\frac{8}{12}=\frac{9}{y}$

On cross-multiplication, the value of y can be obtained as,

  $\begin{array}{c}8y=12\times 9\\ x=\frac{12\times 9}{8}\\ =\frac{27}{2}\end{array}$