Chapter 9.7, Problem 11PSA

To determine

To explain: The Plato’s rule on right angle theory

Answer to Problem 11PSA

His statement is about $45°-45°-90°$

Explanation of Solution

Given information :

The theory on $30°-60°-90°$

Pythagoreans triples are given by the Plato on $45°-45°-90°$ .

He said that in $30°-60°-90°$ are in different ratios and if Pythagorean triples can be formed for such triangle where at least two ratios are same looks beautiful to explain and easy to remember.

So according to Plato, in $45°-45°-90°$ sides of right angle triangle are in ratio of x : x : x $\sqrt{2}$ and he declared the sides of right triangle as $\frac{{\text{m}}^2}{4}+1,\frac{{\text{m}}^2}{4}-1,\text{m}$ for any even number m.