Chapter 9.4, Problem 35PSD

To determine

To find: The ratioof two sides.

Answer to Problem 35PSD

The ratio is equal to $\frac{5}{12}$ .

Explanation of Solution

Given information:

A shortcut along the diagonal of a rectangular field saved a distance of $\frac{1}{3}$ the length of the larger side.

Formula used:

The below theorem is used:

Pythagoras theorem states that “In a right angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides”.

  

In right angle triangle,

  $a^2+b^2\text{= }{c}^2$

Calculation:

  

Let

  $x=$ shorter side,

  $y=$ longer side.

Applying Pythagoras Theorem in right angle triangle, we get

  $\begin{array}{l}{\left(x\right)}^2+{\left(y\right)}^2={\left(x+\frac{2}{3}y\right)}^2\\ {\left(x\right)}^2+{\left(y\right)}^2=x^2+\frac{4}{3}xy+\frac{4}{9}{y}^2\\ \therefore \frac{5}{9}{y}^2=\frac{4}{3}xy\\ \therefore \frac{5}{9}y=\frac{4}{3}x\\ \therefore \frac{x}{y}=\frac{\frac{5}{9}}{\frac{4}{3}}=\frac{5}{12}\end{array}$