Chapter 8.5, Problem 2PSA

Solution

To Calculate: The values of x and y

The values of x and y are $6$ and $5.4$

Given information: Measures of sides i.e., $5,3,10,$ and $9$

Formula used: Here, we are using the concept of angle angle similarity.

Calculation: Here, let one triangle be ADE and the other triangle be ABC

So, In $\Delta ADE$ and $\Delta ABC$

  $\angle A=\angle A$ (common)

  $\angle ADE=\angle ACB$ (corresponding angles)

Hence, $\Delta ADE\sim \Delta ABC$ (by angle angle similarity)

So, $\frac{AE}{EB}=\frac{ED}{BC}$ ( here, BC = y)

➔ $\frac{\text{5}}{\text{3}}\text{=}\frac{\text{9}}{\text{y}}$

So, $y=5.4$

And, $\frac{\text{AD}}{\text{DC}}\text{=}\frac{\text{ED}}{\text{y}}$

➔ $\frac{10}{x}=\frac{9\times 5}{27}$

So, $\text{x=6}$

Hence, the values of x and y are $6$ and $5.4$