Chapter 8.3, Problem 47HP

To determine

To calculate:

The equation of rectangle and draw rectangle.

Answer to Problem 47HP

Equation is $l=\sqrt{3}w$ and rectangle is as follows,

  

Explanation of Solution

Given information:

Condition:

Draw rectangle that has diagonal twice as long as its width.

Calculation:

In a $30°-60°-90°$ triangle, the length of the hypotenuse $h$ is $2$ times the length of the shorter leg $s$ , and length of the longer leg $l$ is $\sqrt{3}$ times the length of the shorter leg.

The diagonal of a rectangle divides the rectangle into two congruent right triangles. If the diagonal is twice the width, then the hypotenuse is twice one leg of the right triangle. This indicates that each right triangle is a $30°-60°-90°$ triangle.

Theorem of $30°-60°-90°$ triangle shows that the other leg is $\sqrt{3}$ times the leg. Thus, the length of the rectangle is $\sqrt{3}$ times the width.

So the equation is $l=\sqrt{3}w$

The rectangle with $l=\sqrt{3}w$ is as follows.