Chapter 9.6, Problem 22PSC

To determine

To find: The ratio of x and y.

Answer to Problem 22PSC

The ratio of x and y is 7:3

Explanation of Solution

Given information :

Given a right angle whose sides are x, 3x + y and 4x − y

Formula used :

Pythagoras theorem

Calculation :

On using Pythagoras theorem, we have

  $\begin{array}{l}{\left(\text{Hypo}\right)}^2={\left(\text{Perp}\right)}^2+{\left(\text{Base}\right)}^2\\ \Rightarrow {\left(\text{4x}-\text{y}\right)}^2={\left(\text{x}\right)}^2+{\left(\text{3x+y}\right)}^2\\ \Rightarrow 16\text{x}+\cancel{{\text{y}}^2}-8\text{xy}={\text{x}}^2+9{\text{x}}^2+\cancel{{\text{y}}^2}+6\text{xy}\\ \Rightarrow 6{\text{x}}^2-14\text{xy}=0\\ \Rightarrow 2\text{x}\left(3\text{x}-7\text{y}\right)=0\\ \text{Since, 2x}\ne \text{0 then}\\ \text{3x}-7\text{y}=0\\ \Rightarrow \frac{\text{x}}{\text{y}}=\frac{7}{3}\\ \Rightarrow \text{x:y=7:3}\end{array}$