Chapter 14, Problem 5CTE

To determine

To construct: a rectangle with width $y$ and diagonal $x$ .

Answer to Problem 5CTE

  

Explanation of Solution

Given information:

Instructed to consider two line segment $x,y,x>y$ and find a rectangle with width $y$ and diagonal $x$ .

Calculation:

First consider such a rectangle $\text{ABCD}$ with diagonal $AC=x$ , and width $AD=y$ .

  

Now from $\Delta \text{ADC}$ ,

  $\begin{array}{l}{\text{AC}}^2=A{D}^2+D{C}^2\\ \Rightarrow DC=\sqrt{{\text{AC}}^2-A{D}^2}=\sqrt{x^2-y^2}\end{array}$

Hence the obtained triangle must have length $\sqrt{x^2-y^2}$ .