Chapter 10.2, Problem 28WE

a.

To determine

To calculate:Construct a segment of length $\sqrt{5}$.

Answer to Problem 28WE

  

Explanation of Solution

Given information:

Draw a segment with length of $1$

Calculation:

To draw a segment of length $\sqrt{5}$ , follow these simple steps,

Step 1: Draw a segment with length of 1, double it in the horizontal direction and take it as it is in vertical direction as shown in figure.

  

Step 2: Now complete the triangle, and the closing side will have length $\sqrt{5}$ ( $\because \sqrt{5}=\sqrt{2^2+1^2}$ )

b.

To determine

To calculate:Construct a segment of length $\frac{1}{2}+\frac{\sqrt{5}}{2}$.

Answer to Problem 28WE

  

Explanation of Solution

Given information:

Draw a segment with length of $1$

Calculation:

To draw a segment of length $\sqrt{5}$ , follow these simple steps,

Step 1: Draw a segment with length of $1$ , double it in the horizontal direction and take it as it is in vertical direction as shown in figure.

  

Step 2: Now complete the triangle, and the closing side will have length $\sqrt{5}$ ( $\because \sqrt{5}=\sqrt{2^2+1^2}$ )

Step 3: Now, extend the line of length $\sqrt{5}$ , to 1 unit and draw a perpendicular bisector to find the midpoint, this half length will be a required length.

  

c.

To determine

To calculate:Construct a golden rectangle whose sides are in the ratio $1:\frac{1}{2}+\frac{\sqrt{5}}{2}$.

Answer to Problem 28WE

  

Explanation of Solution

Given information:

Draw a segment with length of $1$

Calculation:

To draw a segment of length $\sqrt{5}$ , follow these simple steps,

Step 1: Draw a segment with length of 1, double it in the horizontal direction and take it as it is in vertical direction as shown in figure.

  

Step 2: Now complete the triangle, and the closing side will have length $\sqrt{5}$ ( $\because \sqrt{5}=\sqrt{2^2+1^2}$ )

Step 3: Now, extend the line of length $\sqrt{5}$ , to 1 unit and draw a perpendicular bisector to find the midpoint, this half-length will be a required length.

  

Step 4: Now, from the marked half-length segment, and one unit length draw a rectangle