How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle: 6, 12, 18?

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How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle: 6, 12, 18?

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Answer 1 · 2016-02-29T23:34:02

Check the similar triangle with sides $1$ $1$ , $2$ $2$ , $3$ $3$ against Pythagoras formula to find that this is not a right angled triangle.

Explanation:

Three positive numbers can be the measures of the sides of a right triangle if and only if taken in ascending order they satisfy:

$a^{2} + b^{2} = c^{2}$ $a^2+b^2=c^2$

Also a triangle is a right triangle if and only if any similar triangle is a right triangle. So you can multiply or divide $a$ $a$ , $b$ $b$ and $c$ $c$ by any non-zero number before applying the test.

In our example, all of the sides are divisible by $6$ $6$ so let us assign:

$a = \frac{6}{6} = 1$ $a = 6/6 = 1$

$b = \frac{12}{6} = 2$ $b = 12/6 = 2$

$c = \frac{18}{6} = 3$ $c = 18/6 = 3$

We find $a^{2} + b^{2} = 1^{2} + 2^{2} = 1 + 4 = 5 \neq 9 = 3^{2} = c^{2}$ $a^2+b^2 = 1^2+2^2 = 1+4 = 5 != 9 = 3^2 = c^2$

In fact these side lengths only form a degenerate 'triangle' of zero area, with interior angles $0$ $0$ , $0$ $0$ and $π$ $pi$

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How do you use the Pythagorean Theorem to determine if the three numbers could be the measures of the sides of a right triangle: 6, 12, 18?

1 Answer

Explanation:

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