Chapter 8.2, Problem 48PPS

(a)

To determine

To draw: Three different isosceles right triangles.

Explanation of Solution

Given information: The following figure is given.

Drawing: Three different isosceles right triangles is plotted below,

(b)

To determine

To fill: The given empty table.

Answer to Problem 48PPS

The following table is been filled.

  $\begin{array}{ccccccc}Triangles& & & Length& & & Ratio\\ ABC& BC& \sqrt{2}& AB& 1& \frac{BC}{AC}& \sqrt{2}\\ MNP& NP& 2\sqrt{2}& MN& 2& \frac{NP}{MN}& \sqrt{2}\\ XYZ& YZ& 3\sqrt{2}& XY& 3& \frac{YZ}{XY}& \sqrt{2}\end{array}$

Explanation of Solution

Given information: The triangles from part (a),

Calculation: The table has been filled. The ratio and length is been given in the following table.

  $\begin{array}{ccccccc}Triangles& & & Length& & & Ratio\\ ABC& BC& \sqrt{2}& AB& 1& \frac{BC}{AC}& \sqrt{2}\\ MNP& NP& 2\sqrt{2}& MN& 2& \frac{NP}{MN}& \sqrt{2}\\ XYZ& YZ& 3\sqrt{2}& XY& 3& \frac{YZ}{XY}& \sqrt{2}\end{array}$

(c)

To determine

To conjecture: The ratio of the hypotenuse to a leg of an isosceles right triangle.

Answer to Problem 48PPS

The answer is $\sqrt{2}$ .

Explanation of Solution

Given information: The following diagram is given.

Calculation: The ratio of the hypotenuse to a leg of an isosceles right triangle is $\sqrt{2}$ .